There are various patching methods out there and rom hackers use several, it is best to find the release notes/post/NFO/readme that is bundled with the patch and go from there but if not
The extension the patch file uses is usually the name of the patching method and the usual ones are
IPS- old/primitive and not really used for all but the most basic hacks as it has a lot of limitations and tends to be for older roms or as part of a batch (more on that later)
UPS- made as a successor to IPS to remove some limits, has not found much use in the DS world but has some in patches on other platforms.
PPF- originally made for the original playstation I have seen two or three DS patches with it and a slew of Wii ones. Some issues with patch formats changing.
ninja- another potential successor to IPS it did not catch on all that much but I have seen it done.
Xdelta- used by many hackers around here (pretty much as that was what the earlier DS hackers settled upon). No official extension but delta or xdelta or something along those lines is most common (read the patch NFO/release notes/readme and it should tell you).
BSDiff- used more commonly by members of the scene proper for trainer patches but used by a few translation hackers as well. In the larger world of patches BSDiff and xdelta are rivals of a sort although frankly for rom hacking purposes they are as good as each other (they both tend to produce patches small enough for distribution that are fast and do the job).
Batch- DS roms are made of files so some hacks deconstruct the rom, patch the files themselves and rebuild the rom (can make for smaller files than the previously mentioned methods).
DPS- basically a customised batch file and patching method made by deufeufeu for his Jump Ultimate Stars patch. Not sure if anything else uses it.
After this people tend to make their own patching executables or formats (PDS being an example) with the custom patchers you can find.
Frankly though I have just wasted your time. Head on down to
http://www.romhacking.net/?category=2&...itle=&desc= and match up the extension to the description and use one of those. There are a few more frontends around as well if you fancy searching but those on the link should have you covered.