The basics:
Themes only work on 3.2U/E, 4.0U/E, 4.1U/E or 4.2U/E firmware. So if your on anything other than 3.2, 4.0, 4.1 or 4.2 you cannot use a theme. (Note: When using .mym files, 4.0/4.1/4.2 themes are interchangeable, as long as you use the proper base .app. Precompiled themes, or csm/app files, are not interchangeable in version or region. They must be installed on the version and region specified by the creator).
There are different types of themes, some that only have 1 .mym and some with 2 .myms.
Most of the time when you download a theme it will come as a .mym file.  They can come as .csm or .app but .mym is the safest and most preferred way to share.

Making the Theme

Using ThemeMii:
ThemeMii is now a much easier app to use, and is still downloadable (MyMenu is harder to find, because is no longer in service), so this will only cover ThemeMii from now on. You can find ThemeMii here: ThemeMii
If you downloaded a file that is already a .csm or .app then you can just name it according to the install method you want to use (see below).  You actually don't need ThemeMii for .csm/.app files you download (note: you will only find .mym files on this Wiki).


Step 1) If there is a runfirst.mym, in ThemeMii, click File -> Open, and browse for the runfirst.mym. Then, on the bottom right, click "Create CSM". In the file window that opens, look for your base system app (example: 4.1U is Click Open.  Then save this CSM as something conspicuous (like themeRunFirst.csm). If there is no runfirst.mym, skip to step 3.

Step 2) Browse to where you saved your runfirst CSM, and change the name of the extension to .app (note: in Windows, if this was a known file extension, you'd have to have the Folder Options set to show the extension always. For information on how to do that, go here. Luckily for us, .app and .csm are not recognized by Windows!).

Step 3) Now, in ThemeMii, click File -> Open.  Select the main .mym file (name of the theme.mym, usually). Then click "Create CSM again. If there was a runfirst, in the first window, select the .csm you made (renamed to .app). If there wasn't, select your system's base .app (note: ThemeMii has the option of downloading the theme file you're wanting to use via the Tools -> Download Base App menu). In the next window, save the csm as something you'll remember (ThemeMii defaults to "themeName.csm", themeName being replaced with the actual name).

Installing the Theme

Using MyMenuify: (Note: because MyMenuify is simply easier to work with than softmii tweak, this guide will only cover using MyMenuify). Find MyMenuify here.

Note: You will also need to have The Homebrew Channel installed on your Wii in order to use MyMenuify.

Once running, locate and select the theme you're installing (you can put this anywhere on the SD card), click it, click OK (to install), and wait. When its done it asks if you want to exit or continue, hit exit and enjoy your new theme.

If the theme bricks (gives you corrupt files message):
Make sure you used the right runfirst for that theme.
Make sure you used the right default app for your system menu/region. If your sure you used the right runfirst, and the right default app, do it again anyway. If it still bricks let us know and we'll look at it.