To publish an application once you have finished testing it, click on the File menu above the source editor and select Publish Project....
A dialog box will appear in which you can choose the subdomain your application will be served from. You can check if the URL is available by pressing the Check button.
Once you have typed in the application's published name, click the Publish button. This will compile your application into JavaScript and HTML. The files it produces are deployed on Google servers.
After clicking the Publish button, GME will launch the just-published application. The URL that appears in the address bar of your browser is the address to your application and can be distributed to your users.