Put the file in your home directory, Tyler5794, open a terminal and enter
That's it. To start the emulator, open a terminal again and enter
tar xvpf snes9x-1.43-linux-x86.tar.gz
Best to paste and copy my entries: your typing of the package name is a little off... Note that this is a command line version of the emulator. You'll need a frontend as well if you want a GUI.
BTW most people seem to prefer ZSNES to SNES9x - any particular reason for preferring SNES9X?
Edit@TwoWordz: the repository versions seem to be older ones, though, and you appear to be confusing ZSNES with SNES9x.