Google Play now has added direct support for alpha and beta testing applications. Basically, an app can be moved from alpha testing to beta testing to production with ease. You can control who participates in each of these two testing phases. Here are the basic steps.
App Developer Steps
First create a Google+ community and invite the testers. Upon receiving the invitation, the testers should accept the invitation and join the community.
Note down the URL for the community. It will be something like https://plus.google.com/communities/100484486324315756218.
Next, log into Google Play Developer Console. Create the application unless its already created.
Under the APK section, you will now see ALPHA TESTING and BETA TESTING tabs.
Click on the appropriate testing tab. Upload the APK.
Finally, publish the app so that it becomes available in Google Play store. Don’t worry, only the testers taking part in the test program can view the app.
Now, you can control who will participate in testing. Click Manage list of testers.
Enter the URL for the Google+ community and click Add.
Make a note of the share link. Send the link by email to the testers.
A tester will click on the shared link.
Then click BECOME A TESTER.
Then click the download link to go to the Google Play store and install the app.
Moving Through Phases
Once a testing phase is successful, you can move the APK to the next phase.
For example, if the APK is in beta stage, you can click Promote to Prod. Now, the app will be ready for Google review and will be eventually available to general public.