I came across a video a few days ago that show how to get Overdrive ebooks onto your ereader. My local library doesn't have ebooks so this is a topic I couldn't write for myself.
Before you watch the video, you might want to check to see of your library supports ebooks. You can search on the Overdrive website. And it's probably redundant but I just want to make sure that you know that Overdrive ebooks don't work on the Kindle. Amazon won't let it happen (so far).
While we're on the topic, I found a couple cheat sheets you might want to download (here and here). I think they'd make handy reference tools in case you get stuck in the process.