The computer will have open seeks on the seek graph. Just watch for one that fits you wanted time controls and start the game. I imagine there might be some positions where it might hang thinking but generally speaking, you'll have to win by checkmate.
Rated Live Chess Game against Computer?
Miskamole,
If you make sure your Filter is not filtering out the computer challenges you, they will show up in either the Challenges (Graph mode) or Challenges (List mode) tab. However, they disappear rather quickly from there, as play against the computers is popular. However, you can also look them up in the Players tab and directly challenge one of them, as well.
As for the checkmate thing, I don't know. I don't play the computers at all. Hate to get taken to the woodshed by a silicon-based life-form. 
I've played the computer in Live Chess lots of times and it has never resigned so yes, I think you must checkmate it. I've never known it to lose on time either. Playing against it is a generally unfulfilling experience, it sometimes makes bizarre errors, allowing you an easy win and other times squeezes the life out of you. The only reason it's popular is that the latter mode gives rise to its relatively high rating and the former entices people to play it for easy rating points.
How is this done? I can't find any buttons to click on and have seen others playing rated Live Chess games against a computer.
Must you win by checkmate? I doubt that winning on time is a possibility against a machine.