In order to do 3rd gen trading, you must have a GBA Game Link Cable.
As usual, you'd go to the second floor of the Pokemon Center and talk to one of the ladies to go to the Union Room. (There was no GTS in Gen 3)
You'd have to connect two Game Boy Advances with the Game Link Cable, with both of them having any of the 3rd gen games. (Ruby, Sapphire, FireRed, LeafGreen, Emerald)
Then, you'd start trading! :D