Celts certainly had armies. But they were not standing armies, but masses of peasants led by a small cadre of noble horsemen. As they were a very hero-worshipping, "elitist" people, only nobles counted as serious combatants. If a commoner would dare to attack a king, he could be killed by the blazing heat surrounding him. Commoners were there to die.
http://www.maryjones.us/ctexts/mucrama.html
"Well’, said Lugaid, ‘Éogan will now challenge me to single combat and his ardent spirit-[he being] son and heir of the king and grandson of another-will overthrow me’."
From time to time there were duel of champions, of course; in fact, it was often customary to begin a battle with a few such duels.
For normal cattle-raids the army consisted mostly of nobles, but from time to time in great combats the whole people was mobilized, with the women often following the army camp. See eg the invasion of Greece or the battles of Boadicea.
http://en.wikipedia.org/wiki/Battle_of_Watling_Street
http://classics.mit.edu/Tacitus/annals.10.xiv.html
"Nor was Suetonius silent at such a crisis. Though he confided in the valour of his men, he yet mingled encouragements and entreaties to disdain the clamours and empty threats of the barbarians. "There," he said, "you see more women than warriors. Unwarlike, unarmed, they will give way the moment they have recognised that sword and that courage of their conquerors, which have so often routed them. Even among many legions, it is a few who really decide the battle, and it will enhance their glory that a small force should earn the renown of an entire army. Only close up the ranks, and having discharged your javelins, then with shields and swords continue the work of bloodshed and destruction, without a thought of plunder. When once the victory has been won, everything will be in your power."
Such was the enthusiasm which followed the general's address, and so promptly did the veteran soldiery, with their long experience of battles, prepare for the hurling of the javelins, that it was with confidence in the result that Suetonius gave the signal of battle.
At first, the legion kept its position, clinging to the narrow defile as a defence; when they had exhausted their missiles, which they discharged with unerring aim on the closely approaching foe, they rushed out in a wedge-like column. Similar was the onset of the auxiliaries, while the cavalry with extended lances broke through all who offered a strong resistance. The rest turned their back in flight, and flight proved difficult, because the surrounding waggons had blocked retreat. Our soldiers spared not to slay even the women, while the very beasts of burden, transfixed by the missiles, swelled the piles of bodies. Great glory, equal to that of our old victories, was won on that day. Some indeed say that there fell little less than eighty thousand of the Britons, with a loss to our soldiers of about four hundred, and only as many wounded. Boudicea put an end to her life by poison. ... Nothing however distressed the enemy so much as famine, for they had been careless about sowing corn, people of every age having gone to the war, while they reckoned on our supplies as their own."
My favourite quote about the Celtic combat:
http://www.ucc.ie/celt/published/T301035/text021.html
"After Cú Chulainn had been thus distorted, the hero sprang into his scythed chariot with its iron points, its thin sharp edges, its hooks, its steel points, with its sharp spikes of a hero, its arrangement for opening, with its nails that were on the shafts and thongs and loops and fastenings in that chariot.
Then he performs the thunder-feat of a hundred and the thunder-feat of two hundred and the thunder-feat of three hundred and the thunder-feat of four hundred, and he stopped at the thunder-feat of five hundred for he thought that at least that number should fall by him in his first attack and in his first contest of battle against the four provinces of Ireland. And he came forth in this manner to attack his enemies, and took his chariot in a wide circuit outside the four great provinces of Ireland. And he drove the chariot heavily. The iron wheels of the chariot sank deep into the ground so that the manner in which they sank into the ground left furrows sufficient to provide fort and fortress, for there arose on the outside as high as the iron wheels dikes and boulders and rocks and flagstones and gravel from the ground.
The reason why he made this warlike encircling of the four great provinces of Ireland was that they might not flee from him and that they might not disperse around him until he took revenge on them by thus pressing them for the wrong done to the youths of Ulster. And he came across into the middle of the ranks and threw up great ramparts of his enemies' corpses outside around the host. And he made the attack of a foe upon foes among them so that they fell, sole of foot to sole of foot, and headless neck to headless neck, such was the density of their corpses. Thrice again he went around them in this way so that he left a layer of six around them, that is the soles of three men to the necks of three men, all around the encampment. So that the name of this tale in the Táin is Sesrech Breslige, and it is one of the three slaughters which cannot be numbered in the Foray, the three being Sesrech Breslige and Imslige Glennamnach and the battle at Gáirech and Irgáirech, except that on this occasion hound and horse and man suffered alike. Others say that Lug mac Eithlend fought along with Cú Chulainn at Sesrech Breslige.
Their number is not known nor is it possible to count how many fell there of the common soldiery, but their chiefs alone have been counted. "
A description of a duel is here:
http://www.ucc.ie/celt/published/T301035/
"Then the men of Ireland considered what man should be sent to fight with Cú Chulainn in the hour of early morning on the morrow. They all said that it should be Fer Diad mac Damáin meic Dáire, the brave warrior from Fir Domnand. For similar and equal was their power of fighting and combat. With the same fostermothers, Scáthach and Úathach and Aífe, had they learnt the arts of valour and arms, and neither of them had any advantage over the other save that Cú Chulainn possessed the feat of the ga bulga. However, to counterbalance this Fer Diad had a horn-skin when fighting with a warrior on the ford. ...
‘What weapons shall we use now, Cú Chulainn?’ said Fer Diad. ‘Yours is the choice of weapons until night’ said Cú Chulainn, ‘since you were the first to reach the ford’. ‘Let us take then’ said Fer Diad, ‘to our polished, sharpened, hard, smooth spears with their thongs of hard flax’. ‘Let us do so indeed’ said Cú Chulainn. Then they took on them two hard, equally strong shields and they had recourse to the polished, sharpened, hard, smooth spears with their thongs of hard flax. Each of them fell to casting the spears at the other from the middle of the day till the evening. Despite the excellence of the defence, so good was their mutual casting that during that time each of them bled and reddened and wounded the other. ‘Let us cease from this now, Cú Chulainn’ said Fer Diad. ‘Let us do so indeed if the time has come’ said Cú Chulainn.
....
"‘What weapons shall we use today, Fer Diad?’ said Cú Chulainn. ‘Yours is the choice of weapons until night’ said Fer Diad, ‘since I had choice of weapons on the day that is past’. ‘Let us then’ said Cú Chulainn, ‘take to our great long spears today, for we think that thrusting with the spears today will bring us nearer to a decisive victory than the casting of missiles did yesterday. Let our horses be harnessed for us and our chariots yoked that we may fight from our horses and chariots today’. ‘Let us do so indeed’ said Fer Diad. Then they put on two broad, strong shields that day. They had recourse to the great long spears that day. Each of them began to pierce and wound, to overthrow (?) and cast each other down (?) from the twilight of early morning until sunset. If it were usual for birds in flight to pass through men's bodies, they would have gone through their bodies that day and carried lumps of flesh and blood through their wounds and cuts into the clouds and the air outside. And when evening came their horses were weary and their charioteers tired, and the heroes and champions themselves were weary too. ‘Let us cease from this now, Fer Diad’ said Cú Chulainn, ‘for our horses are weary and our charioteers are tired, and when they are weary, why should we also not be weary?’ "
...
They remained there that night. Then Fer Diad rose early on the morrow and came alone to the ford of combat, for he knew that this was the decisive day of the fight, and he knew too that one of them would fall in the fight that day or that both would fall. Then before Cú Chulainn came to meet him, he put on his battle equipment. Of that battle equipment was his filmy satin apron with its border of variegated gold which he wore next to his fair skin. Outside that he put on his apron of supple brown leather, and outside that a great stone as big as a millstone, and outside that stone, through fear and dread of the ga bulga that day, he put his strong, deep, iron apron made of smelted iron. On his head he put his crested helmet of battle which was adorned with forty carbuncle-gems, studded with red enamel and crystal and carbuncle and brilliant stones from the eastern world. In his right hand he took his fierce, strong spear. He set at his left side his curved battle-sword with its golden hilt and guards of red gold. On the arching slope of his back he put his huge, enormous fair shield with its fifty bosses into each boss of which a show boar could fit, not to speak of the great central boss of red gold. That day Fer Diad exhibited many and wonderful and brilliant feats of arms which he had not learned from anyone before that, neither from fostermother nor fosterfather, not from Scáthach nor Úathach nor Aífe, but he invented them himself on that day to oppose Cú Chulainn.
Cú Chulainn too came to the ford and he saw the many brilliant, wonderful feats of arms performed by Fer Diad. ‘You see yonder, my friend Láeg, the many brilliant, wonderful feats performed by Fer Diad, and in due course now all those feats will be directed
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{line 3271-3307} against me. Therefore if it be I who am defeated this day, you must incite me and revile me and speak evil of me so that my ire and anger shall rise the higher thereby. But if it be I who inflict defeat, you must exhort me and praise me and speak will of me that thereby my courage rise higher’. ‘It shall so be done indeed, little Cú’ said Láeg.
Then Cú Chulainn too put on his battle-equipment and performed that day many brilliant, wonderful feats which he had not learned from any other, not from Scáthach nor from Úathach nor from Aífe.
Fer Diad saw these feats and knew that they would in due course be directed against him. ‘What feat of arms shall we perform today, Fer Diad?’ said Cú Chulainn. ‘Yours is the choice until nightfall’ said Fer Diad. ‘Let us perform the "feat of the ford" then’ said Cú Chulainn. ‘Let us do so indeed’ said Fer Diad. But though he said that, it was the feat he deemed it hardest to encounter for he knew that it was at the "feat of the ford" that Cú Chulainn overthrew every champion and every warrior he encountered. Great was the deed that was done on the ford that day, the two heroes, the two champions and the two chariot-fighters of western Europe, the two bright torches of valour of the Irish, the two bestowers of gifts and rewards and wages in the northwestern world, the two mainstays of the valour of the Irish coming from afar to encounter each other through the sowing of dissension and the stirring up of strife by Ailill and Medb. Each of them began to cast these weapons at each other from the twilight of early morning until midday, and when midday came, the rage of the combatants grew fiercer and they drew closer to each other.
Then for the first time Cú Chulainn sprang from the brink of the ford on to the boss of Fer Diad's shield, trying to strike his head from above the rim of the shield. Fer Diad gave the shield a blow with his left elbow and cast Cú Chulainn off like a bird on to the brink of the ford. Again Cú Chulainn sprang from the brink of the ford on to the boss of Fer Diad's shield, seeking to strike his head from above the rim of the shield. Fer Diad gave the shield a blow with his left knee and cast Cú Chulainn off like a child on to the brink of the ford. Láeg noticed what was happening. ‘Alas!’ said Láeg, ‘your opponent has chastised you as a fond mother chastises her child. He had belaboured you as flax (?) is beaten in a pond. He had ground you as a mill grinds malt. He has pierced you as a tool pierces an oak. he has bound you as a twining plant binds trees. He has attacked you as a
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{line 3308-3345} hawk attacks little birds, so that never again will you have a claim or right or title to valour of feats of arms, you distorted little sprite’ said Láeg.
Then for the third time Cú Chulainn rose up as swift as the wind, as speedy as the swallow, as fierce as the dragon, as strong as the air, and landed on the boss of Fer Diad's shield, seeking to strike his head from above the rim of the shield. Then the warrior shook the shield and cast off Cú Chulainn into the bed of the ford as if he had never leapt at all (?).
Then occurred Cú Chulainn's first distortion. He swelled and grew big as a bladder does when inflated and became a fearsome, terrible, many-coloured, strange arch, and the valiant hero towered high above Fer Diad, as big a fomóir or a pirate.
Such was the closeness of their encounter that their heads met above, their feet below and their hands in the middle over the rims and bosses of the shields. Such was the closeness of their encounter that they clove and split their shields from rims to centres. Such was the closeness of their encounter that they caused their spears to bend and turn and yield to pressure from points to rivets. Such was the closeness of their encounter that sprites and goblins and spirits of the glen and demons of the air screamed from the rims of their shields and from the hilts of their swords and from the butt-ends of their spears. Such was the closeness of their encounter that they forced the river from its usual course and extent, and a couch might have been prepared for king or queen on the floor of the ford for not a drop of water remained there except what might drip there with the wrestling and trampling of the two heroes and champions on the floor of the ford. Such was the closeness of their encounter that the horses of the Irish went mad and frenzied and broke their spancels and shackles, their ropes and traces, and women and boys and children and those unfit to fight and the mad among the men of Ireland broke out through the camp south-westwards.
By this time the two combatants were at the edge-feat of swords. Then Fer Diad caught Cú Chulainn unguarded and dealt him a blow with his ivory-hilted blade which he plunged into Cú Chulainn's breast. And Cú Chulainn's blood dripped into his belt and the ford was red with the blood from the warrior's body. Cú Chulainn brooked not this wounding for Fer Diad attacked him with a succession of deadly stout blows, and he asked Láeg for the ga bulga.—Such was the nature of the ga bulga: it used to be set downstream and cast from between the toes: it made
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{line 3346-3383} one wound as it entered a man's body but it had thirty barbs when one tried to remove it and it was not taken from a man's body until the flesh was cut away about it.
And when Fer Diad heard the mention of the ga bulga, he thrust down the shield to shelter the lower part of his body. Cú Chulainn cast the fine spear from off the palm of this hand over the rim of the shield and over the breast- piece of the horn-skin so that its farther half was visible after it had pierced Fer Diad's heart in his breast. Fer Diad thrust up the shield to protect the upper part of his body but that was help that came too late. The charioteer sent the ga bulga downstream. Cú Chulainn caught it between his toes and made a cast of it at Fer Diad. And the ga bulga went through the strong, thick apron of smelted iron and broke in three the great stone as big as a millstone and entered Fer Diad's body through the anus and filled every joint and limb of him with its barbs. ‘That suffices now’ said Fer Diad. ‘I have fallen by that cast. But indeed strongly do you cast from your right foot. "