$ pip install SPLAT-library
Yeah, it's that simple. Just make sure you have Python 3.4 or newer installed (if you have Python 2.7 installed as well, you may need to use pip3). Alternatively, you can download the source code from GitHub and use SPLAT from there; this will only be able to run on the command line, unless you do some magic with the PYTHONPATH environment variable, which I don't suggest.
Pip should handle installing the dependencies for you. If not, SPLAT will try. If SPLAT can't do it, here are the commands you'll need:
You may need to run these commands with sudo.