Act I: To Mondstadt

Set off for Mondstadt, go to the Wangshu Inn
First things first, you need to head to the Wangshu Inn. Use the nearest teleport waypoint and glide down to the restaurant area. You'll trigger a cutscene where you and Paimon spend a bit too much Mora. Mona ends up with barely anything to eat, so you decide to cook her a meal to make up for it.

Look for the innkeeper and ask to borrow the kitchen to make Mona a dish
After the cutscene, teleport back to the top of the inn. Head northwest, go down the stairs, and find Huai’an, the innkeeper. Ask him if you can use the kitchen, and he'll give you the recipe for Golden Crab. Then, head southeast, down the stairs again, and use the stove to cook it. The recipe requires 5 Bird Eggs, 5 pinches of Flour, 4 Crabs, and 2 pinches of Salt. You can buy Bird Eggs from Draff in Springvale, Flour and Crabs from Wanmin Restaurant in Liyue Harbor, and Salt from Mondstadt General Goods in Mondstadt.

Give the Golden Crab (Normal or Delicious) to Mona
Once you've cooked the Golden Crab, head back to Mona in the restaurant and give it to her. She'll then suggest you head to the Stone Gate.

Continue your journey, head for the Stone Gate
Make your way to the Stone Gate using the teleport waypoint. Head northeast down the ramp, and you'll get another cutscene. Some merchants will approach you, offering a ride to Mondstadt since they're heading that way too.

Fend the bandits off
Turns out, they aren't merchants at all, but bandits! This is where the fighting starts. You'll get to use Mona as a Trial Character here. Start by using her Elemental Skill to taunt the enemies and deal some Hydro damage. Then, switch to an Electro character to trigger the Electro-Charged status, dealing damage over time. Follow up with a Pyro skill to trigger Overload, causing an explosion. After the first group is defeated, a second group will appear. Use Mona’s Elemental Burst to suspend them in the air, then repeat the same tactic to finish them off.

Talk to Mona
Once all the bandits are dealt with, speak to Mona. After a short scene, this quest will be completed, and you'll be one step closer to Mondstadt!