To sell items in your inventory to the equipment shop, first enter the equipment shop from the town, and then hit the 'Sell' button next to the character that is carrying the items to sell. At this point you will be given a list of all items that character is carrying (but not those the character is wearing; to sell those things, you must unequip them first) and how much gold the storekeeper is willing to pay you for each. The storekeepers will only give you half of what they intend to resell the item for.