Instructions
Play the game until you acquire the item Pal Pad. This will let you store friend codes, which are sets of numbers that uniquely identify each Pokemon player. Your personal friend code can be found in the Pal Pad, as well.
Exchange friend codes with someone. This can be done online with someone you've never met or with a good friend, as long as they play a Nintendo DS version of Pokemon.
Set a time to meet with the other person, then head to any Pokemon Center in the game.
Go upstairs and speak to the girl at the middle desk. If your friend made it on time, you will be allowed to enter the Wi-Fi Club where you'll be able to see each other and trade your Pokemon.