To do this you either get a free piece of software called Google Play Books, which will integrate with a Google account and allows you to access these from any device with a web browser, or grab yourself the platform-specific app for your device (most devices have Google Books applications).
And it’s free as long as you’ve got a Google account.
I’m mostly posting this as there are a lot of parents getting The Rabbit Who Wanted to Fall Asleep and wondering how they’re going to read it to their kid, but you can use it for any format Google Play Books supports.
To upload a book, you go to books.google.com, my library, and then click upload. It may take it a few minutes to process the book initially, but after it’s processed you can read it from anywhere.
No more being annoyed because Tablet 1 is recharging and Tablet 2 is in the hands of grubby toddler, you can pick up on your phone or a computer.