From everything I can gather, they reckon this should take place in 35 to 50 years. Some reckon sooner of course.
The interesting thing about the timeline is because of the exponential effect of doubling computer speeds, they reckon we will only be half way to the coming singularity when we're only 6- 12 months away from it. People won't even realize. The last doubling effect will carry us much further than we would've imagined in a very short space of time.
When we invent the first computer that is just a wee bit more intelligent than us- it can begin to design the next computer and that one can design the next one ad infinitum until within a couple years time computers are so much more intelligent than us it'll make us look- well- silly. If the computers are benign, they will quickly compute all the solutions to all the things that concern mankind- longevity, cure for disease etc and possibly even show us how to become super intelligent or "trans-human" (I believe is the phrase that many Singularity enthusiasts like to use). After that, supposedly we would become like gods ourselves and could no longer be considered the same species and life after that point is simply unimaginable by the contemporary human of today- hence it being called "The Singularity"- a point it is impossible to see past or speculate beyond.