There are trading stations are on the top floor of the gift shop, to the right of where you can buy weapons. This can be done offline, however guest accounts cannot trade. The controls for trading are:
Press the when indicated to enter the booth, and once both player are inside press to access the trading menu. Scroll and press to select the item to trade, or press to view the other player's items and then scroll through and press to request an item from the other player. Press to accept the trade, then press again after both players have finalized the trade.