When you visit your library, OverDrive will connect you to the library's website. From there, you can log in with your library card number and password. What I've found about my library's catalog is that it's a bit limited. I compare it to NetFlix's streaming content: there's a lot of content, but not a lot of current, must-have books. After you've found the book you want to read, then you choose your delivery method and the checkout period. This is where you need a secondary account link Amazon or Adobe. You can choose what format you would like to read. I prefer Kindle only because I already have an Amazon account. The format you choose will determine where the book is delivered upon download: choose Kindle and it will be in your Kindle app.
I find this next piece pretty cool, and I'm not sure why. When you have reached the end of the lending period, the book simply goes away. Not entirely, but you can't read it anymore. It's still there if you want to purchase it, of course. You can also place holds for books that are checked out. You'll receive an email when it's available and you'll have three days to download it.
Well, that's the basics of OverDrive. Happy Summer Reading!