You should be able to click the Magnifying Glass icon on the bottom-right of the trade window. This will change your cursor to a magnifying glass. You then click on an unidentified item. A prompt should appear, letting you know how much it will cost to identify the item, with OK and CANCEL buttons (or something like that). You click ok, they take your money and identify the item.
If you're at a vendor, you click the Magnifying Glass button, and nothing happens, I'm at a loss. Maybe not every NPC can identify items, you have to take it to an actual vendor? Just guessing.