Talk to Ivanovich, the traveling merchant, at the northern part of Liyue Harbor. You will be asked to write down the instructions on how to get a business permit.
Follow the quest trail to get to the bulletin board. When you're there, select the third option: "Let's look for news about new business permit applications..."
Talk to Ivanovich again and he will give you instructions on who to give the documents to.
Head east from Ivanovich's location to find Nervous An and give him the exit permit.
Go up the 2 sets of stairs into the main city area, and give milelith Jiayi the business premises and safety certificates.
Lastly, talk to Clerk Zhao and give her the old business permit.
Once you are done, talk to Ivanovich again to receive your quest rewards of 100,000 Mora and 10 Adventurer's Experience.
Puzzles, Secrets, and Hidden Chests in Liyue
Ragged Records Hidden Quest Guide
Puzzles, Secrets, and Hidden Chests in Dragonspine
Violetgrass Farming Map
Treasure Lost, Treasure Found Quest Guide
How to Farm Character Ascension Materials