Before you get started
Do not use this to cheat online, and do not attempt to play a certain game online if you cannot run it in Dolphin at full speed.
Nintendo's Wi-Fi Connection service, along with all other GameSpy-powered services, shut down on May 20th, 2014 . Most online-enabled games will not immediately be able to connect online because of this.
Wiimmfi was created in an effort to preserve these servers for various games, and many of them can be played online again thanks to it. If you want to try out a game that connected via Wi-Fi Connection, check it out. However, be aware that Wiimmfi is not meant to be used with Dolphin. Players who aren't emulating the system at full speed constantly while online will be banned from the servers. There are ways around this, but it's best just not to try again with a certain game if it does happen while playing it.
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\
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.