This page of the Elden Ring game guide explains whether it's possible to use Fast Travel in the game, and if so, what is necessary to use it.
Yes, there is fast travel in Elden Ring, but it works slightly differently when compared to previous From Software games. To use fast travel, you first need to discover a Site of Grace.
Then, instead of resting at the site of grace, you need to open your map. You can fast travel by using the map and markers. Most of the places you can teleport to using the map are previously discovered sites of grace. Fast travel costs nothing, but it makes previously defeated opponents respawn.