Only the games using nintendo's servers (well, more precisely the one who used gamespy servers) need a private server now.
There are still games officially working online.
You don't need to mess up anything if it's already softmoded.
To connect to private servers you need to edit the server's URL in the game.
It can be done manually (patching the ISO) or in memory (letting a loader do its magic at game launch).
Like greywolf said, USBLoaderGX has option for private server patching.
HTTPS only : remove the SSL certificate requirement. needed if you want to connect to altwfc server. you need to edit the DNS in your settings
HTTPS+wimmfi : edit both SSL and the URL to connect to wimmfi.de server. No need to edit the DNS.
in both servers, your existing profile/friendcode will not work.
You will have to re-create a new driving license for Mario kart, etc.