Leave your safe house (or any other building you are inside) and walk out onto the street. Taxi cabs in the game only appear on the street.
Walk around until you find a taxi. Taxis spawn randomly throughout the game, so it may be a few seconds before you find one. Just like in real life, taxis are four-door yellow cars marked "Taxi" or "Cab" (depending on the company).
Walk up to the back seat of the taxi cab. Press "Triangle" to enter. If you walk up to the front seat you will steal the taxi, which disables your ability to teleport.
Select your destination from the menu that appears when you're in the taxi. You can select the locations of any of the characters you have met in the game or choose a custom destination.
Press "X." The screen will fade out. Your character will teleport to the destination you have selected. The screen will fade back up. Press "Triangle" to get out of the taxi.