Once the aircraft involved has passed, you enter the runway, line up and wait. You'll get take-off clearance as soon as he has vacated (normally).
If ATC wants you to hold short of the runway until the aircraft has vacated, you'll get a "hold short" instruction, followed by a "cleared take-off".
There was a thread here about a related subject "ready for departure" about a month or so ago. Lots of good info on that one.