Always use the UNHEADERED (UH) version of the hack for the practice rom.
The patch file with "Savestates" in the filename is only intended for SD2SNES, FXPAK, and Super NTs (with "jailbreak" firmware). It may cause crashes or serious graphical errors if used with emulators or Everdrives.
The most commonly used tool to apply .IPS patches is [http://fusoya.eludevisibility.org/lips/ Lunar IPS], but you can also use [https://www.romhacking.net/utilities/1040/ Floating IPS], [http://www.romhacking.net/utilities/18/ SNES Tool], [http://ucon64.sourceforge.net/ ucon64], or [http://projects.sappharad.com/tools/multipatch.html MultiPatch], among others.
Some patches might come in other formats besides IPS. [https://www.romhacking.net/utilities/1040/ FLIPS] can handle both .IPS and .BPS formats, while [https://www.romhacking.net/utilities/598/ xDeltaUI] will take care of .xdelta patches. Another option is a web-based patcher like RomPatcherJS (this might particularly help those of you stuck on mobile).
Regardless of which tool you use, the process is the same: you select the .IPS file and an original ROM file, and it will replace the original ROM with a patched ROM. Then simply load up the patched ROM in your emulator or flash cart of choice. If all goes well, you're done and can delete the .IPS file if you like.