Wiimmfi is a custom server that replaces Nintendo's WFC servers which were shut down in 2014. It is based off of Brainslug. The service has full support for 242 games, works with some issues on 11 games, and 255 games currently in testing.
Ways to run
The app can be downloaded and installed on an SD card or USB to load via the Homebrew Channel. Running it performs a one-time patch on a disc, after exiting the game, the patch no longer works and the app has to be run again to patch it again. Using a custom DNS in the settings, set the DNS server to 220.127.116.11 and then go to the EULA agreement. It should load the Wiimmfi patcher.
Finally, if the Internet Channel is usable, go to http://chadsoft.co.uk/wiimmfi/ and bookmark it in the channel. Then load it through the bookmarks. This may or may not work.