You have to create a google group (or google+ community). Then your Dev Console will generate a link. Provide that link to your users, they will have to join the community first and then they can download the app (which is going to be listed in the BETA TESTING section of APK).
The first time, I didn't notice the new button after uploading the APK in the Beta-Test section.
I understand now how to do:
- I register the email address of the user in my Google group
- I send an email to the user with the opt-in URL (that could be the welcome msg of the group)
- He opens the opt-in dialog (I have to warn him not to take the displayed text into account)
- He clicks on the button to become a tester
- He goes to Google Play and can download the app
I'm a bit worried to have to maintain a different version (one more) and by the fact the user is considered as a tester.