Instructions
Defeat the first Pokemon Gym leader in the game in Violet City to get the Zephyr Badge. This makes obtaining the Pal Pad possible.
Go to any Pokemon Center and go down to the basement to find the Wi-Fi Club. Talk to the assistant, Teala, and she will give you a Pal Pad.
Log onto the Nintendo Wi-Fi Connection and you will be given your unique Friend Code, a 12-digit number.
Get the Friend Code of the person you want to connect with and enter it into your Pal Pad. Give them your Friend code and get them to enter it into their Pal Pad.
Log into the Wi-Fi Club when you are both connected to the Nintendo Wi-Fi Network and you will be able to connect with the other person for Pokemon battles and trades.