disclaimer:
first: this is not the best way of doing it this is just a easy to understand begginer method doing it with wiimms iso tools is better but is not a begginer method
second: this does not work with all mods but works most of them
tutorial:
1: get the game rom the format dont matter much only needs be recgonized by dolphin emu
2: get the riivolution mod
3: open dolphin emu and add the game there
4: right click on the game and go to properties->file system then right click the disc and select extract entire disc (how you are using dolphin the dump is quite bad so if the file "opening.bnr" or most of the mod files are missing do the dump again but with the computer disconnected from the internet) now select a folder for the game be dumped (if it is empty higher the chance of a better dump)
5: now you need to mannually overwrite the original game files with the mod files (do NOT change the file extension if it is not the same exept for ".er" or ".brstm")
6: open dolphin again and add another game this game go to "\folder you dumped the game\data\sys\" and select to check on sub directories just for be sure
7: right click the game that should be saying that is 0 bytes now select convert file and make sure that the first option is iso and dont change anything else
8: use wii backup manager to convert your iso back to wbfs
9: done