Ah - I see your confusion.
It’s a common purchasing system used in RPGs, but is not explained for people who have not encountered it before.
In this screen, you see “stuff you own” on the left, with the text at the top, “Player inventory”, hidden behind the health/mana display (BUG! Oh well…).
On the right, you see “stuff that the shopkeeper owns”, split into the stuff she’s selling on behalf of each of the three factions (The Expedition, The Deep Elves, The Shamblers).
Between them, there are two 3x3 grids.
The one on the left, by your stuff, is marked “Your offer”.
The one on the right, by the shopkeeper’s stuff, is marked “Request items”.
If you want something from the shopkeeper, drag it from her wares into your “Request items” grid. If you want to offer her something in return, drag stuff from your stuff into the “Your offer” grid. You won’t get full value from it: maybe a half or quarter. It shows how much she’ll buy your stuff for, and how mush she’ll sell her stuff for, in the “value” labels above those two grids.
The difference in value will be made up in coins: if you offer a couple ripper pomes worth a total of one silver, and ask for a runebag worth 15 silver, then you’ll end up paying 14 silver when you complete the trade, which you can do by clicking on the “Trade” label under the two grids.
Because that’s secretly a button, even though it looks identical to the other labels around. Which, thinking about it, is probably where you got stuck.
I mean, even looking at that screenshot, I had to go back into the game to figure out how I completed the trade, because I couldn’t remember! Was it E? Space? Nope. Only clicking the text “Trade”. Which does change on mouseover, but that’s the only clue.