Whenever you encounter another adventurer, or the target of an "I want it!" quest, you can trade with them. Trading allows you to trade one of your equipment or items for the other hero's equipment or item.
When you open the trade window, you will see their inventory, including wielded items. Choosing one will bring up either a list of items in your inventory that has equal or higher value than the item you just selected, or will exit the trade window, if you don't have anything worth what you're asking for. However, be careful as the game will trade an entire stack. So if you have a stack of 10 cure corruption potions and you select it, then the game will hand over the entire stack instead of just one potion.
Trading allows you to exchange your high value equipment, which have a 95% price reduction at a shopkeeper, for items you might actually use. However, gold is weightless, while equipment you might be carrying around in the hopes of finding an adventurer with something you need is not. Stacks of cure corruption potions and scrolls of oracle have a small amount of weight for a high amount of value, as do engagement jewelry.
Note that characters with the pickpocket skill are able to set the other character up for an easy take by trading low weight high value items for heavy ones. This allows the character to trade for the heavy equipment desired, followed by pick pocketing the low-weight traded item back. For example, trading a stack of Scrolls of Oracle for the Miracle Knight Helm <Silly Name> allows for a quick and easy theft of the scrolls back, netting the character both the helm and the scrolls quite handily.
If you trade for a cursed or doomed equipment which the NPC has equipped, the NPC will manage to somehow take it off and hand it to you, despite the fact that this should be impossible. This is useful if an adventurer has equipped an item with the "it attracts monsters" attribute, in order to prevent hostile monsters from attacking town NPCs.
A note on trading potions: if you trade a potion, the NPC won't drink it. However, if you then give (via nteraction) another potion which stacks with then traded potion, the NPC will the proceed to guzzle down the entire stack, one after the other.
In Elona+, trading a non-weapon item for an adventurer's equipped weapon (either in hand or ranged slot) will always make them generate another weapon to fill that slot immediately. The newly generated weapon is usually of great quality, and even rarely artifact.