Be aware of the items placed in the other player's inventory at all time. If both of you do it, the trade will execute successfully. Once you reach an agreement over the goods, you should click the check button, it will turn green once you do.

There, both of you can put what items you have to trade in your respective inventories.

You will see your inventory space on the left side of the window, and over it, the other player's inventory. The other player will have to accept your trade request in order to open the trading window. Select the player you want to trade with by left-clicking with your mouse, and an option to trade will become available. Note that you can only trade while being in the town of the respective chapter ( Rogue Encampment, Lut Gholein, Kurast Docks, Pandemonium Fortress or Harrogath). You don't need to be in party to trade, just to be in the same game. You can also adjust the Maximum number of players and the difficulty. you have to give the game you create a name, you can input a password for it (optional), and you may also write a description, where you should write what are you trying to trade. To trade, you have to create a 'Trade game' or join an already created trade room.

Diablo 2 marketplace wiki