How long does it take for languages to diverge from each other to a point where they are no longer mutually intelligible? Is there some distance where a languages will begin to separate, how does technology, population and terrain influence this distance?
Historical Linguistics is the modern science of determining how languages change over time. This site goes into considerable detail about the process, but in practice since language is continually evolving, you might find difficulties in as few as 200 years. Certainly I have found it difficult enough to converse with Americans, Britons and Australians (indeed as a Canadian in a multi-national force, I sometimes had to act as a translator between them!). Other studies have been done and general rules for how quickly languages drift have been discovered, for example Grimm's Law
However, for languages to become mutually incomprehensible would take a great deal longer. Proto-Indo-European (PIE) may have been spoken by everyone in the region of modern Ukraine @ 3500 BC, but it seems that even PIE had already significantly diverged after 1000 years, and even the linkage between PIE daughter languages was only teased out in the 18th century. A very good book which reconstructs the spread of PIE is The Horse, the Wheel, and Language, and the author all makes some well educated estimates on how rapidly the language diverged.
So putting all these together and thinking of even the changes in English over the time span of that language, we can see some quite significant shifts coming after only a century or two. By 500 years, only specialists could read the language (think of reading or performing a Shakespearean play as written in the 1500's for an audience today. Chaucer's The Canterbury Tales, written in the 1300's is even more difficult to read or speak), and after 1000 years, the language would be all but incomprehensible (Beowulf, written over 1000 years ago, needs to be extensively translated for a modern audience). If two groups of speakers from the original language were isolated for these lengths of time, the resulting dialects would probably be considered new languages.
So the lower limit is probably 500 years and a reasonable limit would be 1000 years for a language to have diverged enough to be mutually incomprehensible.
Social factors (including isolation due to terrain, invasion, cultural interchange) are very influential here, and there are some laws/trends.
The most well documented is that the more isolated a community the more conservative their language remains. Hence Sardinian is the most conservative daughter of Latin, East Coast American dialects of English are closer to the English spoken in 16th and 17th century England than modern British English, and 12th century Icelandic is completely intelligible to modern Icelanders (similar to reading Shakespeare for us). The pronunciation has shifted quite a bit meaning that 12th century Icelanders and modern Icelanders actually talking would have a little more difficulty - but would still be able to communicate.
English is a very different kettle of fish - we've had invasions (Norman and Norse having profound affects on the language to the extent that some say English is a sprachbund - an approaching-equal descendant of different mother languages) and cultural and social changes and borrowings from languages all over the world due to being at the centre of things. There's no chance that Beowulf can be read by modern English speakers because Old English was literally destroyed and regathered itself into Middle English through the 11th and 12th centuries - Chaucer would have had nearly as much difficulty with Beowulf as we do - by the 14th century Middle English was an unintelligible separate language from Old English.
The type of written record the language uses (or doesn't use) is important too. Literary Chinese is incredibly long-lived in that texts from the very distant past are slightly intelligible to modern Chinese, and with more language study this effect increases. However, the spoken language has evolved wildly in a similar time so that speakers separated by a similar time distance would have no chance of understanding each other, even if they were speaking the (ancestor/descendent of) the same dialect.
As well as asking in linguistics, try the ZBB ('zompist bulletin board' - a resource for making constructed languages and constructed worlds, and a general resource for linguistics learning) - they are very knowledgeable and will point you to actual scholarship. www.incatena.org
The bottom line is - think about your social factors. Isolation will slow linguistic change in a population. Conquest can combine and even destroy languages, though substrates will remain. The world is your oyster with regards to world building possibilities - you can create the conditions for your people to be able to understand writings from thousands of years ago without too much trouble - or you can separate a population from its ancestors of even 100 years by an impregnable intelligibility barrier.
The amount of time it takes for a divide to appear is proportional to both the amount of intercommunication between speaking groups, and the volume of written material produced.
An extremely isolated group without a significant literary corpus can diverge in just a few generations. A highly interconnected group with significant written record will diverge less rapidly.
These are not the only factors, though. Significant changes in social, economic or technological status can spur rapid linguistic changes, which may lead to divergence or consolidation depending on whether those changes are unifying or divisive.
For more detailed answers, consider asking over at linguistics.
I am not a language researcher; but I have read (New Scientist, I believe) that linguistic researchers have observed divergence that apparently occurred in a single generation, as the result of a revolution: As I recall, a population had a civil war; split in two, and the "rebels" intentionally modified pronunciation, gender assignment rules, and some fundamental words like for family members (son, daughter, father, mother). Man, talk about being pissed off ... we don't even want your stinkin' language!