When SpaceX recovers the Falcon 9 first stage at sea, roughly how much time passes between lift-off and soft touchdown on the barge?
This depends on the exact flight profile. For the upcoming (hopefully today's) DSCOVR mission launch, expected first stage landing is at T+09:20 (liftoff is at T-0, which is not exactly the case for all launch vehicles, but the difference would still be up to a few seconds at most). For the SpX-5 cargo mission to the station, this ETA was at T+09:45 (reentry was slower from insertion into LEO that it will be from the flight profile for the higher energy trajectory towards Sun-Earth Lagrange point 1's insertion, so next reentry will reach roughly 2x the dynamic pressure than the previous one - i.e. initial first stage descent will be faster too).
So, on average, the Falcon 9 first stage is expected to land downrange on ASDS (Autonomous Spaceport Drone Ship) roughly 9 and a half minutes after liftoff.