I will not attempt to comment on military aspect (how was a Gallic warhost organised) as I do not feel I have read enough specifically on Gallic tribes and their wars to be able to comment, and I am nothing remotely approaching a military historians. Instead I will focus on Caesar's depiction of the Gallic armies.

Caesar's Commentarii de Bello Gallico is a part of what we refer to as the Posidonian tradition, classical writings about the Celts as a whole, and includes authors such as Athenaeus, Diodorus Siculus, Strabo, and, of course, Posidonius himself, although his writings are lost. It is clear that the other authors heavily exploited Posidonius' writings. With the exception of Caesar, it is unknown how much, if any, contact was sustained between the other authors and the Celts, and we need to recognise that there is a distinct possibility all their accounts were simply culled from Posidonius' writings and contain no personal experience; the sheer physical distance between the writers and the Celts, or any of the barbarians, limited interaction and fostered a situation in which factual information about the Celts was scarce.

As we are left with no historical records from the Celts themselves, it is impossible to validate or refute anything the classical authors ascribed to their culture, however, many historians believe that their depictions of the Celts can be understood as following the archetype of the noble savage. (Edit: It has been pointed out to me that the concept of 'White Man's Burden' is potentially more fitting here. I will retain the original answer but amend WMB to the rest of the response.)

The archetype of the Noble Savage/the concept of the White Man's Burden is utilised to invalidate the culture of specific ethnic groups whose conquest is either greatly desired, or to romanticise conquered groups who are no longer regarded as a threat. It must be understood this definition was not created by conquering people's as a means to an end, but later prescribed to their activities and their writings where the oppressed "savage" groups are concerned. It attempts to define and categorise human behaviour when dealing with people who are perceived to be inferiors. This model provides an explanation of why a people need to be colonised and civilised as well a motivator as to why the effort should be made to do so.

The Posidonian tradition's establishment of the continental Celtic peoples as barbaric, tempestuous and vicious but also passionate, intelligent and valiant follows the archetype of the Noble Savage/White Man's Burden: a people who are uncivilised but inherently valuable to the conquering society. The Gauls are poorly disciplined and lacking in military organisation, but they are exceptionally brave and skilled at fighting. They were a people to be admired, but who should not and could not be trusted to live without Roman rule.

The violence of all Celtic peoples, not just the Gauls, are thoroughly discussed in the Posidonian tradition: they fight at feasts, they head-hunt and carry the heads of their slain enemies with them on their horses or display them in their homes, and they partake in human sacrifice. They are boastful, vain, greedy, jealous, warlike and barbaric.

But at the same time, they are brave and intelligent. Strabo and Diodorus Siculus both comment on the intelligence and proclivity for education of the Celts. Caesar, more than any of the other authors, was fascinated by the Druids and discusses them at length. Their importance and their skill, both legal and divine, is emphasised by all the writers.

So do we trust them? How accurate do we believe these accounts to be? We cannot possibly ascribe a personal agenda to Strabo, Athenaeus and Diodorus Siculus, and although more difficult to determine Posidonius' personal biases and intentions, there are those who believe his depictions of he Celts were philosophical propaganda: his descriptions of Druids can be seen as nothing more than attempt by Posidonius to enforce Stoic doctrine and create evidence to demonstrate his own personal theories.

As for Caesar, his motivations are easier to imagine, as he was looking for a justification for conquest. Caesar was not a historian; he was a warlord who created the political propaganda he needed. Caesar needed to establish a reason for conquering the Celts. He needed to demonstrate their barbaric practices, their ferocity in battle and their bravery, not only to create a reason to subdue them, but also to create a worthy opponent, whose defeat would bring him glory.

Caesar discusses their political situation, stating there are political parties "in almost every home," and as this sounds tenuous and unstable, the Celts' propensity for battle and this unsound situation would have been a solid justification to go to war: subdue them before their fragile politics lead them into battle, either against each other, or Rome. Outside of wanting to take them over and create glory for himself, Caesar needed to create a benefit for the empire. He needed to demonstrate what would be gained by amalgamating the Celts. This is why he discusses the druids so thoroughly, why he emphasizes the Celts' bravery: he needed to make them appear valuable.

How accurate is his image of the Gallic armies? I wish I had firm answers and I encourage you to do more reading and form your own opinions. As for myself, I think it is mostly propaganda, and I think all of the writings of the Posidonian tradition need to be read skeptically, and critically.

Sources:

Cunliffe, Barry. The Ancient Celts. London: Penguin Books, 1999

Fairchild, Hoxie Neale. The Noble Savage. New York: Columbia University Press, 1928.

Rankin, H. D. Celts and the Classical World. North Ryde: Croom Helm, 1987

Tierney, J. J. "The Celtic Ethnography of Posidonius." The Proceedings of the Royal Irish Academy 60 (1960): 189-275.

Williams, Derek. Romans and Barbarians. London: Constable and Company Ltd, 1998

For a collection of the relevant writings of the Posidonian tradition (in translation) see:

The Celtic Heroic Age, ed. John T. Koch and John Carey. Aberystwyth: Celtic Studies Publications, 2003.

Follow up - why was their individual fighting prowess so great? If they lacked a competent commander or training how did they become such fearsome warriors?

Goldsworthy says that the Gauls lacked training and discipline but could form tight formations on the field (e.g. the Helveti are depicted in a phalanx with overlapping shields). Their army movement would be clumsy with over-encumbered trains and many non-combatants slowing them down.

Their lack of organized logistics meant armies had very little staying power before they ran out of local supplies and had to disperse. The southern and central tribes had a little more organization meaning they could stay in the field a bit longer.

They possessed some rudimentary siege craft due to the importance of the oppida in Gallic warfare as a central supply point.

Their cavalry were better having a higher morale and possessing the four-horn saddle which the Romans later adopted. However poor discipline meant rallying from pursuit was difficult and their scouting was poor.

The infantry used body shields, helmets, and the richer men wearing mail shirts. Some fought naked according to Diodorus but gives no numbers or context (I wonder if he's lumping in Gauls with the Gaesatai). I should point out that this type of arma (shield, helmet, sword, javelin) is roughly comparable to what the average milites throughout much of the Republic's history less the chest pectoral.

The core would be the leaders and their retinue (G is not sure if loyalty oaths existed or the Germanic custom of not outliving their leader was practised). Gathering the army would then take time however as news would have to spread about the muster and then the men would need to travel there. Large tribal alliances could mean multiple little armies joined together into a massive host.

Because of their logistical constraints, the goal was to fight a big decisive battle and attacks on towns were threats to force that battle. Only a strong leader (e.g. Vercingetorix) could hold an army together while avoiding battle, compel allies to provide supplies and organize the transport, and wait for the perfect opportunity.

It should be noted that, while in general the Gallic armies showed less discipline than the Roman's, the legiones weren't perfect robots and we have examples where the much vaunted Roman discipline breaks down. At Thapsus Caesar didn't want to initiate battle and "[h]e was bawling out constantly that he did not approve of engaging in battle by an impromptu sally, and repeatedly checking the line from advancing, when suddenly a trumpeter on the right wing, yielding to pressure from the troops and without Caesar's orders, began to sound the call to charge. This was taken up by all the cohorts and they began to advance on the enemy, but the centurions faced about and vainly attempted to restrain their men, urging them not to engage without their commander's orders." (African War 82) You could even lump in the behaviour of Pullo and Vorenus who charged outside of their camp in an effort to amass more personal glory - at great risk to themselves and to their unit's morale and cohesion if they had died.