First, download the latest version by clicking the download zip button to the right. After downloading, extract the contents of the zip to the below directory. Restart Garry's Mod and you're all set!
If you wish to install the latest and greatest version, head over to the develop branch. You can download the zip or clone the repository using Git. This will allow you to play on the bleeding edge, and - if you fork to your own space on GitHub - contribute back to the project.
Creating a Server
After you have installed, launch Garry's Mod and select the Prop Hunt gamemode from the dropdown in the bottom right. From there, create a server as you normally would.