Method 1. Installing from DEB File

The quickest and easiest way to do this is to download and install the lone DEB file from Bearoso's personal repository. Make sure all dependencies are met prior to installation.

wget https://sites.google.com/site/bearoso/snes9x/snes9x_1.60-1_amd64.deb && dpkg -i snes9x_1.60-1_amd64.deb

Now, keep in mind that as of the date of this post, the latest stable build of snes9x is currently at 1.61, and there are some changes since then. If you're upgrading, make a backup of your snes9x.conf file and check the second method below for replacing the binary.

Method 2. Building from Source

You'll need to get certain packages installed:

apt install build-essential cmake git glslang-dev libgtk2.0-dev libgtk-3-dev libminizip-dev libsdl2-2.0-0 libsdl2-dev meson portaudio19-dev

Clone the git repository, build, and install (feel free to change --prefix=/usr/ to --prefix=/usr/local, if preferred):

cd ~/snes9x/
git clone https://github.com/snes9xgit/snes9x.git
cd snes9x/
git submodule update --init shaders/SPIRV-Cross
cd gtk
meson build --prefix=/usr/ --buildtype=release --strip
cd build
ninja
sudo ninja install

If all went well, your snes9x should be ready to go, and with your backed up snes9x.conf file, apply your changes to the new file.

Another method is to use the nightly builds and choose either snes9x-gtk or snes9x-x11 platforms, and then just move the executable binary to /usr/bin/ or /usr/bin/local/, and then launch it as snes9x.