If you're on Linux you will need three things - a copy of the FFVI ROM file (it's left up to the reader to find a copy); a patching program that supports IPS patches, which almost all general web or desktop patchers will; and a SNES emulator. There are several for Linux, but I personally recommend bsnes. It is a very accurate emulator with some nice features, such as displaying Mode7 graphics in higher fidelity (which this game utilizes).

I can second bsnes. At least for me, snes9x has annoying audio stutters I couldn’t seem to get away from. bsnes also has (IMO) nicer looking upscaling ootb.