If you click on the trade icon during your chat with a trader this trade window will pop up. You click on the item you want to sell on your char's side and click on the trader item if you want to buy something. bot items then move into the trade area. If you want to balance it out with money, click on the balance scale on his or your side (the tiny icon underneath the char pics) - if you hit "agree", the deal is done. But you have to pay the amount the trader wants, you can't pay/offer less. Though the skill "trader tongue" and the opinion the trader has towards you lowers his price and increases yours.

Some traders offer "identify": click on the looking glass and you will see all your unidentified items on your side. Click on them and pay the price.
Some traders offer "repair": click on the hammer and you will see your items highlighted in red, the ones that have been damaged. Pay the price.

For these 2 transactions you need money, so if you have expensive items in your loot and want to sell them, I advise repair first, he has enough money to pay you then - if you find no items in his inventory you want to trade
Trade goods are respawned after a while - but you can save and reload before entering the shop and have a look. Even the goods display is random.