You cannot trade with the wireless (unfortunately). However, you can battle with it.
Basically the wireless link is used for the Union Room. From the Union Room you can play minigames with people, battle them, and chat with them. I've only got one copy of Fire Red and one copy of Leaf Green so I'm not sure if you can chat with more than one person in the same window (a la MSN invite two have multiple people) or not. (anyone have a copy that's going to be at the Sandy, Utah City Championships tomorrow?).
It's nifty though. Joe Monkey and I were playing with the Union Room Chat a whole bunch last Saturday at League. You can do all sorts of nifty stuff with it. I'll try to get a screenshot of the Union Room chat tonight.
EDIT: Oh I forgot to add. The Union Room is the person on the left in the 2nd floor of the Pokemon Center. You have to have a Pokedex and at least 2 pokemon in your party to be able to enter.