The Trip Through Fog and Wind world quest in Genshin Impact takes place in the Golden Apple Archipelago, and players will need to complete it if they want to get to the island in the very northeast corner of the map.
The first thing you need to do is spawn at the teleporter on Twinning Isle and drop straight down off the cliff in front of you. Glide down and you will notice a ledge and a crack in the cliff that you can go inside about half way down. Inside, smash the breakable rock that is blocking your path and you will find a desk with some Illegible Notes on it. Read them and the Trip Through Fog and Wind quest will be added to your world quests. Make sure to select it from the list in your menus if you need to.
From there, you need to make your way to the waypoint shown in the northeast of the map. Once there, set in the in-game time to between 10 AM and 14 PM and you will be able to follow a route on the surface of the water through the fog. There will be some rocks and whirlpools to move around, but this is fairly simple.
When you get to the end, you will have arrived at the island in the very northeast corner of the map. Jump out of your both and climb to the top of the short cliffy island to find three Precious Chests and a mural on the wall. Interact with the mural to finish up this quest and get a new one called The Other Side of Isle and Sea.