The Metro Train is a great way to get around! Its a fully working transportation system that brings you all over Los Santos! Its free to use as well!
Taxi services are available in one of two ways, either call them on your phone by pressing F1, then left arrow for services, and select Taxi. When you send them a message your GPS coordinates will be sent to them. Otherwise, you may call the AI Taxi by type /taxi in chat. Be wary though that the AI Taxi sometimes may not get you to your destination in one piece which is why you may want to make sure a human taxi is on first before you try the AI. Check the Playerlist by pressing F9 and seeing if there are any human taxis online.
*NOTE, if you have the taxi speed and run red lights, you the passenger will be held liable for all fines if a police officer catches you. The officer may decide to also issue jail time if you do not stop the taxi within a reasonable amount of time. (Remove the current waypoint, and place a new waypoint closeby to have the taxi drop you off as the police officer wants to talk to you and most likely issue a ticket)