Note, we have written detailed guidance on using Google Classroom with Book Creator, so check that out if you are interested in looking at workflow options.
This article shows you how to use the share button on a published book to quickly send your book to Google Classroom for students to read.
Publish your book first, so you have the online link to the book (note, you won't see the share button in the Read to Me mode unless you've published it)
From there, click on the Share button in the toolbar
Choose Google Classroom
Choose how you want to share the book from the options provided
Note, using this method, you'll only be able to give students the option to read the book, they won't be able to edit it. You'll need them to join your library to do that (more details in the link above).
You'll notice that the share button also gives you the option to share the link to Facebook and Twitter, as well as Embed on your website and Print.