For the most part ROM hacks are distributed as patches because distributing the whole thing would be copyright infringement if it is not a ROM shared by the devs for it, a lot of bandwidth and harder for people to stack multiple patches or have options in patching.
They are usually quite simple to apply (find relevant patching program, tell it to use this patch on this file, press go, wait for it to patch it), though I am not sure what one it would have used in this case.
Anyway common patching formats should it not include information on what it needs
1) IPS. Not used much for DS games as it has limitations that make it not work with common approaches for DS hacks. Extremely popular on the GBA and older cartridge and floppy disc based consoles though. I quite like
https://www.romhacking.net/utilities/13/ myself but there are hundreds of patchers available, including many emulators themselves.
2) Xdelta (no official extension but many will call it .xdelta or .patch or something similar). Couple of main versions for it depending upon the age of the hack of choice of patch maker.
https://www.evanjones.ca/software/xdelta-win32.html and
https://github.com/jmacd/xdelta-gpl/releases should get you them. You might have to tell it to ignore source verification as it will try to check the ROM you are using to see if it matches the one it thinks it should be using and if you trimmed it, used a redump that might have changed something minor, hardcoded a cheat, used that anti AP tool going around to in turn try to run the ROM on a DSi/3ds without a flash cart, or used another patch on top of it (won't always work but we can cover that another time).
3) BSDiff (usually seen with the BSD extension).
https://www.pokorra.de/coding/bsdiff.html should have binaries for it.
4) PPF. Older format (stood originally for playstation patching format) but some people used it on the Wii. Few different versions I see floating around so you will have to find the right one here. There will be a few in the downloads section here and the romhacking.net site above will have some others.
5) UPS. Designed as a replacement for IPS this got used for a handful of GBA games (mother 3 being among the more notable), still has limitations that mean it did not get used for much beyond that.
6) Something more custom. Usually for when someone wants to have a lot of options available to the would be hack user. This should be included in the patch download but you never know.
The download link or the readme/nfo/patch notes included in the file should contain info on what needs to be done.