From YPPedia

If you're looking for trade as it applies to the economy, go to trading.

Trade allows pirates to exchange inventory items and PoE with other pirates. On doubloon oceans, pirates may exchange doubloons as well. Some items such as badges (except the pirate badge), as well as exclusive box edition items (savvy hat and backsword) are untradeable.

Using the Trade Interface

To initiate a trade request, click on the pirate you wish to trade with and select the Trade with icon. It looks like this:

If the other pirate has their Do not disturb enabled, you'll see something like this, and cannot initiate a trade request (unless they are one of your hearties):

The pirate you requested a trade with will receive a notice on their Ahoy tab, and can choose whether to negotiate or reject the request. Should they accept, you'll see something like this (doubloon line appears on Doubloon oceans only):

If you wish to trade Pieces of Eight, just enter a number in the top line. To trade doubloons, enter a number in the second line. If you should go over the number you have in either when entering a number, it will change to the amount you are carrying. To trade items, access your booty panel, and drag the items into the trade window. You can trade more than two items at once, a scrollbar will appear if needed. Items that are untradeable cannot be placed into the item boxes, nor can items being worn or wielded.

If you deem the trade terms acceptable, click the Ready checkbox. When this box is checked on your side, you cannot alter anything in the boxes. If you have it checked and the other pirate changes their terms, it will automatically uncheck on your side (to avoid pirates scamming each other with last minute changes). The checkbox cannot be checked for about three seconds after the other pirate has made a change.

When both sides have clicked the Ready checkbox, the trade goes through. If either side clicks the Reject button, the trade aborts.