Android - How can I read my epub books in Google Books for Android?

As of March 2013, Google Play Books supports third-party ePub or PDF files. You can upload books to your account by visiting in your web browser (when logged in to your Google account, of course). You are permitted to store up to 1,000 uploaded files on your account at a time, and each file must be no larger than 50 MB in size.

There are also many alternative book reader apps that support ePub files if you would prefer that. Aldiko seems to be very well liked, but I have not used it myself.