I cannot figure out how to sell items. The manual doesn't say, and I cannot find the answer through any internet search. I believe I've tried everything in game, but nothing! Please help...

Pretty much just like buying things but in reverse. When in a shop, open a chest. Drag the item you want to sell from your inventory to the chest inventory.

Note that shops will only take certain items; if its price is listed in green you can sell it, but if it's red you can't. There is a shop or two that takes any item but they aren't in the city, so you'll end up using the city traders the most anyway.

Also note that different shops will offer different prices for things, and that the inventory of any given shop will always be constant; that is, it never resets after you buy something. Once an item is purchased, it stays purchased, and stores do not restock. On the plus side, they also don't sell your stuff, so you can get things back if you need to.