I agree with Scott Helme's point in another answer here. But in some extreme situations (security issues, API breaking changes...) where you absolutely need the users to update to continue using the app, you could provide a simple versioning API. The API would look like this:
When your app starts, you could call this API that pass in the current app version, and check the response of the versioning API call.
true, show a popup dialog with options to either let user quit the app, or go to Google Play Store to upgrade the app.
true, show the pop-up dialog with options to update or to continue using the app.
Even with this forced upgrade ability in place, you should continue to support older versions, unless absolutely needed.