These days I do most of my reading on my Kindle Fire, and whenever possible I grab e-books from my local library. Because, you know, they're free.
If you've never checked out a book this way, or you're still doing it the "old way," you may be surprised to learn it's quite easy. You don't need to download a file to your PC and "sideload" it into your Kindle or anything like that. In fact, you don't need your PC or Mac at all.
What you do need is a Kindle Fire and one particular library-friendly e-reader app. Here's how to check out an e-book straight from your library to your tablet. (Note that the process is quite similar for checking out audiobooks, but for purposes of this tutorial, let's focus on the stuff you read.)