OverDrive made reading their eBooks on a Kindle--or any Kindle App--a reality this week. As a Librarian, the most articulate thing I can say is, "Wow!"
Getting an eBook from OverDrive to a Kindle is a little different than getting it onto a Nook or other EPUB-centric eReader.
You don't need Adobe Digital Editions, and you don't "side load".
I've put a basic set of instructions up on this site in the Cheat Sheets section and in the Staff Tools and Resources section.
But let me repeat my main point: "Wow!"