It's very easy.
To install the mod, simply cut & paste the folder "beast" (extracted from the mod latest download) to your Mods folder, that can be found in your Shadowgrounds main directory by default.
Then run the Shadowgrounds Launcher, choose from the dropdown list titled Mod Selection mod Shadowgrounds: Beast, press Activate Mod, and Launch the game.
To use your own save games (and profiles) in the mod, copy your own Profiles folder to beast folder, overwriting the beast mod Profiles folder in the process.