Extremely little. The sum total of evidence we have for the druids could probably on a few pages. All that comes down to us directly are a handful of references by Roman authors, non of which actually sets out to describe the druids, the mentions are all incidental. here is a fairly typical example, from Pliny the Elder 30.4:

The Gallic provinces, too, were pervaded by the magic art, and that even down to a period within memory; for it was the Emperor Tiberius that put down their Druids, and all that tribe of wizards and physicians. But why make further mention of these prohibitions, with reference to an art which has now crossed the very Ocean even, and has penetrated to the void recesses of Nature? At the present day, struck with fascination, Britannia still cultivates this art, and that, with ceremonials so august, that she might almost seem to have been the first to communicate them to the people of Persia. To such a degree are nations throughout the whole world, totally different as they are and quite unknown to one another, in accord upon this one point!

Such being the fact, then, we cannot too highly appreciate the obligation that is due to the Roman people, for having put an end to those monstrous rites, in accordance with which, to murder a man was to do an act of the greatest devoutness, and to eat his flesh was to secure the highest blessings of health.

The broad context of this passage is not a description of Gaul or even religious rites, but a discussion of magic--the previous section describes the defunct Italian magical practices, the next section is about soothsaying. This is how most descriptions of druids go--offhand mention, usually connecting them to strange magical rites.

The exception is Julius Caesar, who gives an extended description of Gallic society in Book VI, chapters 13 and 14 of which describe druids. There is a fair amount of largely insoluble discussion about whether or not the account is reliable: for me, I find it largely plausible. What is interesting about Caesar's account is that he describes the druids as an essentially civic office deeply involved in the political an social life of the community rather than simply weird magicians. In fact, one of the most important Gallic allies of Caesar, Diviacus, was a druid, so when we think of druids our best, most complete source describes them not as wandering mystics but as almost clergymen.

EDIT: Rewrote this bit:

Outside of classical sources we can also use medieval Welsh and Irish legends and archaeology, but both of these have problems that are in many ways even deeper than with classical sources. Archaeology's problem is simple: it is largely non-existent. Archaeology can and has confirmed certain pieces of the classical accounts such as the use of human sacrifice (although bog bodies is a specifically Germanic practice) but it cannot tell us specifically about the druids. No artifacts (such as sickles, mixing bowls, or mistletoe formed material) can be correlated to classical accounts. There are a few items, most notably of the Deal Warrior, identified as Druidic, but there isn't really good reason behind the identification, Plausible, sure, but not really backed up.

The other main source would then be later legends from the Welsh and Irish, which have the advantage of being a more interior view than Roman authors, but unfortunately possess the weaknesses of being from a Christian perspective and being much later. Because the mentions of druids are largely in hagiographic accounts, they are largely cast as the antagonists of missionary saints, and their social role becomes reduced to magician and soothsayer. This doesn't make them useless, and if nothing else it testifies to the enduring importance of the druidic order, but we need to be clear that the interests of the writers was not an accurate and fair minded portrayal. The other problem is chronological distance: these accounts were written after druids had essentially ceased to exist, and more importantly, many centuries after the Roman conquest created a fundamental change in the social and cultural landscape of the Celtic world. That druids still existed throughout the Roman period and beyond is virtually undeniable, but sporadic persecution and a realignment of political institutions means they would not have occupied the same role. This may explain why druids are portrayed in myth as wandering mystics and sorcerers rather than integral members of communal politics.

So in short we don't know much. I put stock in Caesar: the were an integral part of socio-political life and they formed a complementary institution to the growing "secular" power of chieftains and kings. They derived a great deal of their authority from education, extra-communal ties, and ritual power. Beyond that it is very difficult to say.

If you want a good introductory source, see Barry Cunliffe's Druids: A very Short Introduction.

Ogham was a script rather than a language. There is some information on it here, (PDF, pg 351) and here (PDF). BTW, the Unicode standard is a great work of scholarship, and fun to browse.