You can run restaurant if you have Restaurant Deed which can be puchased from Governer Finn at Goverment.
You have the deed, you can craft foods for your restaurant.
You can craft food you have enough material. You can check all recipes right side of the screen. Most food recipes need plantable things, fruits and fish.
If you want to earn money, you need to have enough food in stash. Then press [O] to open your restaurant.
If you run out of stock, your restaurant will be closed.