In order to play games on Core, you must have Core installed on your PC (or Mac if using Bootcamp). Go to coregames.com and click the "Download Core" button in the upper-right corner of the screen to download the Core Installer:
Installing and Launching
For completing the installation and launching Core, check out this article.
Registering Your Account
Once you have Core installed, you will also need to register an account to begin playing games.