They have to give it to you. The only way to even remotely"take", is to sell items via Trade when NPC's store is open.
Receiving money/gold for services or haggled goods has been my biggest issue as well. It works, but not reliably. Personally, I've found the inconsistency not worth the hassle and just sell ores and herbs I collect.
Still, like the game a lot though.
The market. I believe it's the Thalassar market, which is the name of the capital to the east. Mirel is the one who hauls it over every night around 12pm.
When you first start a new game and spawn in you should start near a crate and market stall by the road. Clicking on the stall shows the price you can sell to the market for the day and the crate lets you deposit the items you want to sell. Payment is received over one or more days at 6 AM via aerial delivery.