Overdrive is a library loan of e-books and audiobooks. Most libraries in my area have it, and a lot of patrons have e-readers to use it. You can use it on a regular computer, but most people use either a dedicated e-reader, a tablet or a smartphone.
There are many, many different types. Kindles, Nooks, iPads and Android tablets being the most popular. As for the easiest to use, I'd have to say a Kindle Fire (the Amazon Tablet) or an Android device (either tablet or smartphone). Nooks have to be hooked up to a computer to use Overdrive. iPads are also pretty easy, but it doesn't get easier than the Kindle Fire, since you don't have to download anything to use it.
With an Android, you can either download the Overdrive app, or the Kindle app. Either work. With the iPad, I think you can only have the Overdrive app. I'm not sure if you can get the Kindle app for it, but I wouldn't be surprised if you could.