Airborne time is taken on trust, though we have the records from the tower to go on if someone is doing a local flight.
There some new things on the market that will end any ambiguity, basically a hard drive that records flight time and is then downloaded when you return to base.
Most people are basically honest though, so it's rare you have a problem, though I usually notice any issues from the fuel burn. If it looks significantly out, then I'll have a dig about, otherwise we rely on honesty.