4 main classes of cheating for the 3ds, not counting the leaked network info stuff like the pokemon battle analyser. In basically all cases you will want a homebrew capable 3ds that can run custom firmwares, I say this mainly so if you only have a sky3ds or equivalent.
1) Save editing
2) RAM editing
3) ROM editing
4) Some kind of cart based cheat
Save editing is mainly the domain of the Datel powersaves and that Japanese save editing thing as well. Some people have made save editors/viewers (
https://gbatemp.net/threads/wip-sm4sh-save-editor.382699/ being one such thing) and the hacks are at such a level that you can do things like this.
http://3dbrew.org/wiki/Savegames if you do want to do things here.
RAM editing. The spider thing linked earlier is the most general purpose offering right now. Many of the other "custom" firmwares offer ram viewing and editing which is much the same, however most of said same custom firmwares are not focused on piracy so there may be some stumbling blocks there. Animal crossing has a more worked up thing for it right now. There is an emulator you could attach a process viewer to so as to figure some things out but for the most part you are doing it in hardware.
ROM editing. You can edit the binaries of 3DS games. If you found the lives value was at some location and then you looked through the code and found something that subtracted from that location then you could change it into an add (or make it do nothing) -- not usually a hard trick
http://imrannazar.com/ARM-Opcode-Map . Alternatively you could add a routine to keep that location topped up ever vblank or something (this is what your traditional action replay does).
Both of those approaches have been used for years, here is one such guide for the DS
https://gbatemp.net/threads/crackers-ds-trainer-maker-tutorial.44410/ and the main difference will probably be you are using
http://3dbrew.org/wiki/Memory_layout rather than
http://problemkaputt.de/gbatek.htm#dsmemorymaps
The cart based cheat stuff I have not looked into so much and it right now it is the sole domain of MT card and is terrible. I don't doubt gateway could do something in the future but meh.
People seem to be wondering if mario kart has
cheats and if it does then I suspect 2) and 3) have been done. It is kind of surprising that GBAtemp had not heard about it if so but hey.