Here's how it works. On mobile, search for the book you're interested in and click the "Get Book" tab that appears right up top, just under the book's info. You'll then see where you can buy the e-book and below that, which libraries have it available. On desktop, the purchasing and library information appears on the right-hand side of the screen, just scroll down to get to the library bit. Once you click your library, you'll need your membership information to log in and get the book.
Google is packing more and more into its search features these days, but this option is pretty convenient and could save you a trip to the library, or at least a search step. The feature is currently US-only and is rolling out now.