Shopkeepers stand behind their counters in town and trade in gold. Right click one, or hold your thumb on them, and choose to buy or sell.
Who sells what
The general store has food and potions for the road. The armoury sells armour for every class as it grows into it. The people who teach the trades sell replacement tools and bait, so a lost pickaxe or rod is never the end of a trade.
Buying
Pick an item, choose how many, and press Buy. If it will not fit in your bag the purchase does not happen and you keep your gold. A shop never runs out of stock.
Selling
Open the Sell tab and offer something from your bag. The shopkeeper says what they will pay before you agree.
What a shop does not sell
Everything on a shelf is the ordinary tier with no upgrade. Better gear is found in dungeons, made by players or pushed higher with Charge Dice (see upgrading your gear).
Next: the bank, for whatever you bought and cannot carry.