Tom, from everything I'm seeing, you can't import epub (or any other) format books to "Google Play Books" (yes, that's a dumb name). My guess is that you'll need an alternative app for this.
The more I research, it does appear this is the case. Ok, so first impression with books (and yes a slight jab here), the "closed" iPad lets me bring my own books into the book application made by the same company who made the OS. The "open" Google side doesn't. I'll still do some reading in Google's app as they did include a free book to do a direct comparison with iBooks. I know Kindle is the answer for a lot of folks, just my preference to stay away from their closed system.
One positive too (going to be honest both ways ;), and a feature I'd like to see on iOS: The ability to install an app the way I just did with your Cool Reader link. I'm here on a desktop computer, clicked a web link, clicked install, confirmed the device it should go to, and it's installed without touching the tablet or using a program.
My initial impressions of Android this time around are much better then the attempt back in 2010. On the positive side, the speed of the UI does seem much improved (but also agreeing with Andy, not to iOS levels yet).