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 only play one game turn at a time. When you start playing a new game turn, the old one will be saved into its TRN file, and stopped. You can, however, restart it at any time you wish and continue where you left off.
You can also explicitly stop playing a game turn using the Pause button on the game list. This will also save the TRN file and stop playing. However, if you just want a TRN file, you can just download it through the file manager. The file manager is synchronized with PCC2 Web, and will always create a current TRN file for you when you want one. Note that when you play a managed game, you should use the Pause button to submit the turn file to the host system.