The Dorgesh-Kaan market trading minigame is where you can sell food to Gourmets by the price you sell it for. If you sell it for a price too low they think something is wrong with it, on the flip side if you sell it for something over-priced they will not buy it.
Before being able to sell foods, you will need to get permission first. This is done by speaking to Lurgon, owner of Dorgesh-Kaan General Supplies - he can be found wandering around the middle of the market. He will explain the basics of trading and inform you that you will need permission from the Dorgeshuun Council first, with a certain (random) councillor in charge of the marketplace. Find this councillor and ask for permission, which you are granted instantly. Return to Lurgon - you will now be able to sell food to the goblins.
Show the food to the Lurgon, he will tell you the price that Gourmets are ready to pay.