Genshin Impact's map is quite large, so being able to quickly navigate it through fast travel is a blessing. The good news is that there are also plenty of fast travel points for you to explore, allowing you to set up an extensive network of teleportation points.
The first thing to keep in mind is that you should always be on the lookout for waypoints that will allow you to travel quickly as you explore the world. The map is covered with them, and the more you find, the more efficient your playing time will be.
This map was created using https://genshin-impact-map.appsample.com/#/To activate the Fast Travel Points, you will need to interact with them once, which will earn you XP as well as setting up the new waypoint. You can also quickly travel to other sites, such as the Statues of the Seven.
To travel fast, open your map and click on one of the fast travel points you have already discovered. This will bring up information about the area and also a prompt to get there quickly. Press the prompt button at the bottom right of the screen and you will be taken to your new location.
And that's all. Fast traveling to Genshin Impact is not a complicated system, but it is quite useful. As always, make sure you're constantly on the lookout for new fast travel points, as some of them can be hidden in weird places, like on top of ruins or giant pillars.
