Fast Travel in Tom Clancy’s The Division is a bit hidden and can easily be overlooked. When you open the world map and scroll over an icon check the top left corner to see if there’s a button prompt for fast travel. This is only available for certain locations, such as: Base of Operations, Main Missions, Safe Houses, HUBs and other players in your group. Basically all large settlements that are shown on your map with an orange icon will work.
It’s unavailable while inside the Dark Zone!

While hovering over an icon on your map press the following buttons to confirm fast travel:

• PS4: press Square and then X to confirm.
• Xbox One: press X and then A.
• PC: press whichever key is used for reloading weapons and confirm with the key that lets you place markers on the map.

Now you will see an arrow pointing to the destination and a loading icon shows up. After a few seconds the screen fades to black and you respawn in the destination area.

You can even use fast travel while inside main mission buildings. It works from anywhere, except the Dark Zone (Red area on map where PvP takes place). Please note that you cannot fast travel to encounters, collectibles, miscellaneous objectives and other small locations.
It’s available from the beginning and there are no special requirements. You only need to have visited the location once.