As a passenger
Taxis are player-driven and there is no way to call one. You flag a driver down in the street — if nobody's on shift, nobody's coming. Fare is set automatically by distance and pays out when you exit.
As a driver
Walk into the Taxi Depot and start a shift. You need a B-class driving license. There's no deposit — the cab is free to take out. Ride offers come to the Taxi app on your phone (it only appears while you're on the taxi job); claim one, drive them where they want, get paid (income-taxed like any other job).
No NPC fallback (yet)
There is no NPC taxi driver. If nobody's on shift, the bike rack or walking are your only options. Bus drivers run fixed routes when on shift but routes don't reach the driving school directly.