Yeah we are going to need to have a link to the patch.
Wii patching takes on a variety of forms owing to the way things work there, which also makes it somewhat more annoying in some cases than older devices where "get right version of iso, get patch, get patcher, press go" tends to be it.
Anyway three broad schools of thought for Wii patches
1) Some made some kind of hack that applies the patch directly to the game/via the game.
Smash Brothers is probably the more notable of these today but there are others. Some patches will be exclusively this for whatever reasons the devs of the patches imagine (some kind of anti piracy stance, no sense of irony and want their hacks to remain unhacked in turn, mistaken belief that this is the superior method and no others need be considered)
2) Needs the files pulled from the iso, patched individually and reinserted.
Wii games as seen by the Scene are encrypted unlike most things before it. This means many will instead opt to rip individual files from the iso such that they are in their unencrypted state and then inserted, or the iso further converted to another format.
3) There was a notable component of the Wii homebrew/ROM hacking/iso running scene that opted out of big encrypted files and instead went in for the WBFS and related formats, or indeed scrubbed isos of various formats that would also trouble the traditional patch approaches that expected a fixed base game. Today you can just about convert from WBFS or whatever else back to plain iso though it is a long winded process.
Anyway part of that means basically 2) again and you pull individual files out according to a list, patch them and shove them back in.
Some will have scripts to do this for you as well (the files might end up in essentially random locations depending upon the tool used to make the wbfs or whatever but the names and directories should remain the same such that you can do that approach). This will need whatever OS the scripts were made for (typically Windows) or you to understand what each step does in the script and replicate it in your OS of choice (should be able to do it happily on Linux, if you are a filthy OSX user then might just about be able to get it done with online patching tools, android is a possibility as well but will be annoying).
Oh and there is also the Wiiware/VC patching fun, plus gamecube, but that is a different discussion (though basically method "2)" again but instead of wii scrubber or
https://wit.wiimm.de/ you use showmiiwads or whatever tools people are using to pull apart such things these days).
xdelta is a popular patching method which, like most patch methods these days it seems, has a couple of mutually incompatible versions out there.
Old school xdelta is
https://www.evanjones.ca/software/xdelta-win32.html
Newer stuff
http://xdelta.org/
There are tools that have nice graphical user interfaces.
I have also seen old IPS be used (it is an awful format for Wii stuff but can work in some limited cases), again many versions of IPS out there but I generally go for
https://www.romhacking.net/utilities/13/ (might have to put *.* in the name part to force it to see all files)
Seen a few bsdiff things
http://www.daemonology.net/bsdiff/
Seen a few PPF (short for playstation patching format, as in PS1) for reasons known only to the modders making them. romhacking.net above has a bunch of these.
Seen a few other more exotic formats at least in discussions as well.
This is all why people are telling you to look at the readme that will come with the patch, or if someone removed that (some bad download sites will strip such useful data) then find the release post or a better download.
