Midnight, you are correct. Once you have added your friend's code and they have added yours, you both must search for "Friends", and you will be connected with each other.
For convenience, Nintendo added a nice little feature for determing when your friend is searching. If, while you are on Wifi at any time, you see a little blue box who up in the lower right corner of the top screen, followed by a small sound, that means that a friend is looking for a game. Then you can go to Friends and search for them.