It's actually easy, but you have to borrow a book from your Kindle, you can't do it online. You also have to be an Amazon Prime member, which is a great deal. Seriously.
Amazon can deliver a Heinz Organic Tomato Ketchup Twin Pack to your front door in two days!
You can't beat that, but that's not important right now.
Here's how to borrow a Kindle book on Amazon:
Eligible Amazon Prime members can borrow books from the Kindle Owners' Lending Library directly on their registered Kindle device.
Image: Courtesy Amazon.com

You can borrow one book per month.
Note: All links are amazon.com affiliate links where I make a few cents if you click through and buy something.