The "Play" item on the navigation bar will provide a list of all games you play on PlanetsCentral, as well as games you uploaded using the File Manager. If you didn't upload all required files yet, or didn't yet assign a game directory to a hosted game, the games will be listed under Need Work and offer an option to complete the setup.
When everything is complete, PlanetsCentral will offer you a Play button in the Play section, and directly in the file manager.
The Play section also offers you a demo game, which you can try while not logged in.
You can play different games in different browser tabs, but not multiple tabs for the same game. If you open a new tab with a game, the old tab will disconnect from the server.
When you're done playing (for now), use the "Save & Exit" button to exit the PCC2 Web application. This will save a turn file to the game directory, and, for a managed game, submit it to the host system.