The first thing you learn in linguistics is that languages evolve.  The second is that they are arbitrary.   This does not mean language isn’t important, or that it isn’t integral to culture. (see this article on Quebec’s policing of language).  It does mean that there is nothing inherent in the word ‘spoon’ that denotes the rounded tool with which you cook or eat.

Medieval Welsh, or Middle Welsh, was the language spoken in the 12th to 14th centuries.  Like when a modern English-speaker attempts to read Chaucer in English, it is possible for a modern Welsh speaker to read middle Welsh, which is the language of much of the Welsh literature (Four Tales of the Mabinogi, for example) that we have, although the tales themselves are much older.  You can find out about learning it here:

http://www.celt.dias.ie/publications/cat/cat_h.html#H.2

The root of the changes between medieval and modern Welsh lie in what linguists call ‘mutations’, mostly in initial consonents.  This site (http://www.chass.utoronto.ca/~klausner/MUT.html) can help with that.

Old Welsh, on the other hand, is different yet again and not readily intelligible to Welsh readers.  This language dates from around 800 AD to the 12th century.   It is important to point out, however, that it is very hard to know if the pronunciation of words changed as much as the writing changed.  We cannot hear people reading these ancient documents out loud.  They may have pronounced words similarly to modern Welsh, but simply spelled the words differently.

Primitive Welsh dates to 550 AD, and derives from what linguists call British, or Brythonic, one of the Celtic insular languges which also includes Breton and Cornish.

http://www.ethnologue.com/show_family.asp?subid=1166-16

This language borrowed heavily from Latin, not surprising since Rome ruled Britain from 43 to 411 AD.   An easy example of this is the Latin word, ‘draco’, which becomes ‘draig’ in Welsh and ‘dragon’ in English.  Many of these words with Latin roots have to do with religion, again not surprising given the use of Latin in the Christian Church:  “Sacramentum” has become sacrafen; “episcopus”, esgob; “ecclesia”, eglwys; “altar”, allor; “Caresima”, Carawys; and so on.”

http://www.newadvent.org/cathen/15532a.htm

The language spoken by the earliest Britains can only be guessed at as some proto-Brythonic, pre-Celtic language.  The people of Britain, prior to the coming of the Romans, were not literate, so there is no record of them or their history, beyond the material remains uncovered by archaeologists.