This can be done by completing the following:

1. Invite the player to your party.
2. Navigate to the player's name in the bottom left portion of the menu.
3. Choose the "Invite to Trade" option.
4. This will bring up the trade menu where you're able to see what items are available for trading, what you're willing to trade along with the other member.
5. A request must be made by one player and the other player must accept the request for a successful trade.

Note: This can not be done with a split screen party member.

Here is a video as a source:  

This can be done by completing the following:

1. Invite the player to your party.
2. Navigate to the player's name in the bottom left portion of the menu.
3. Choose the "Invite to Trade" option.
4. This will bring up the trade menu where you're able to see what items are available for trading, what you're willing to trade along with the other member.
5. A request must be made by one player and the other player must accept the request for a successful trade.

Note: This cannot be done with a split screen party member.

Here is a video as a source: