The simplest way to get postActiv is to download the archive file of the Master branch, which is our stable branch and you should be able to reliably install it in pretty much any environment that can run PHP and MySQL or MariaDB.
Get the master branch download here, and then just upload it to the web root on your respective webserver. If you are using Windows, it's usually best to unpack the archive prior to uploading it on the server.
Alternatively, you can also run the Nightly branch of postActiv, which is the bleeding-edge development branch. Be warned that this branch should be considered unstable and you use it at your own risk! The download for that branch is here.
You can also browse the previous versions of postActiv here, if you wish to run a specific older version.
For the latest installation and configuration information on postActiv, read the respective files available here and here.
If you wish, instead of downloading the archive to your server, you can use the git svcm software to keep your version of postActiv up to date. Instructions on how to do so are in the Installation documentation linked above.
Do you own a BeagleBone or compatible system? Then you can also install postActiv through the FreedomBone distribution by Bob Mottram. You can find how to do so here and how to get FreedomBone itself going is explained here.