Dolphin Online
Before you get started
While most people here don't care about pirating or fucking with people, please don't use this to cheat online, and don't attempt to play online if you can't even run the game on Dolphin at a stable 60 VPS (fullspeed). All you'll do is fuck up everyone elses game, and possibly make Nintendo look into shutting everything down - ruining it for everyone actually Nintendo is shutting down online service for Wii on May 20th, 2014 anyway [1]. If you want to help create an alternative, take a look here and collect some data packets.
Requirements
How to
Simply copy over the certs into Dolphin's directory, the .pem files go to Dolphin\User\Wii\
Note: If you're using a newer build of Dolphin without portable.txt these files need to go into My Documents\Dolphin Emulator\User\Wii\
Playing online
You should now be able to get online with any game that supports Nintendo WFC, and play online like a normal Wii would. It should also be noted that this isn't perfect yet, so there will be crashes and disconnects.