Somebody mentioned Audacity but that isn't really something you'd use for composing/making music, you instead mainly use it to edit a sound file you already have.
If you want pure SNES music then you can use Mario Paint Composer which is a PC program for composing music just like the musical minigame/feature in Mario Paint on the SNES
http://mario-paint-composer.en.softonic.com/
However, you're pretty limited with what you can do with this so it's more something to have a play with rather than something to make serious music out of.
The most used composition software (to my knowledge) is FL Studio which has heaps of features and plugins, but it isn't free unfortunately (costs $99). There is a free demo that you can try out though:
http://www.image-line.com/flstudio/
If you hunt around you may be able to find the earlier version of FL Studio called Fruity Loops which is completely free but obviously doesn't have as much stuff and is no longer supported. I don't have a link for it unfortunately.
Another option is MuseScore, which I prefer over FL mainly because the music is written in traditional music notation (staves and whatnot) which is easier for me, but might be different for you. This one is free and open source so you're free to make as much stuff as you like in it. Not sure how well it supports 16bit sounds though:
http://musescore.org/
I guess lastly you can always get a MIDI keyboard (the instrument, not the one you type with), a synthesiser and recording equipment, then play something directly into your computer. It's probably the hardest and most expensive option but might as well mention it as well:
http://www.musicrepo.com/recording-a-keyboard-on-computer/
As for how to use any of these things, there are plenty of tutorials online that I'm not gonna elaborate on because we'd be here all day. :P
Anyway, hope that helps!
