This is the coolest reason to use *hax. You can run modified version of games using an app called HANS. Things like music mods or texture swaps are easy, but you can also make new levels for games or add in completely new features. There are a few limitations though. You can't use update data with HANS, and you need a copy of the game in question, and a full dump of it, to make a romhack. You can patch update data directly into the rom loaded by HANS, but you need a 9.2 3DS to get update data legally at the moment.

 

 On the subject of dumping the games, you can use this app, but it will take ages and you will probably need a bigger SD card. Some games won't work, like The Legend of Zelda Triforce Heroes, or Animal Crossing Happy Home Designer. Once you have the Romfs and Exefs, you can use the romfs extractor and builder including in this pack these tools to extract and build the romfs. You shouldn't need to mess with the exefs for most things. 

 

 If you open HANS with the game you want to mod selected, and turn on romfs loading, there will be a line of text showing you where to put and what to name the romfs it will load. So name the custom romfs as specified and put it in a folder titled "hans" on the root of your SD card. I recomend taking the SD card out of your 3DS and putting it in your computer (located under the back plate on the n3DS) since these are big files we're moving.