On this page of the guide to Halo Infinite you'll find detailed information about how to unlock fast travel and how to use it correctly. You'll also learn about situations in which fast travel could be blocked.
Fast travel availability
Fast travel isn't available initially. It can't be used during the first campaign missions, as they require you to visit consecutive linear areas. It can also be temporarily blocked later on in the game, for example, while you're visiting the interiors of larger structures.
Fast travel becomes available as you explore the surface of Zeta Halo's ring. You can learn about fast travel's current status thanks to the message in the lower-right corner of your Tacmap - Offline means fast travel is blocked, Online means it can be used freely.
Fast travel requirements
You can use fast travel to move to Allied locations - captured enemy fortresses and FOB bases. By opening the map and moving your cursor onto an area's icon you should see information about fast travel being possible to activate on the bottom of the screen (an example pictured).
After pressing the X button you must confirm you want to fast travel. Fast travel is free and doesn't use any resources, but Master Chief will always "teleport" alone, without any AI-controlled soldiers he may have been accompanied by.