Free applications for Android phones can be found at the Google Play Store. The Google Play Store has its own website as well as a mobile app that comes preloaded on all Android devices.
To find free applications from a mobile device, go to the Play Store app, click the Apps tab once the Play Store is loaded, and click the Top Free tab to find the top-rated free applications. To find a more specific free application, click through the Categories tab to find the Top Free tab for each app category. The same steps work to find free applications from the Google Play website, but you need a Google account to access and download the applications.