To call a taxi, position Niko near traffic--preferably somewhere on the sidewalk. Spot a cab and press LB (with an Xbox 360 controller) to have Niko automatically call out for a taxi. It is also possible to order a taxi with the cell phone if you have problems spotting one. Additionally, Niko can eventually earn the ability to call a limo as you progress in the game.
You can also approach a taxi that already has a fare from the passenger side, then pull out the passenger and get in.