You download ADE from
http://www.adobe.com/products/digitaleditions/
Once installed you'll need to authorise your computer, part of this process requires you to create an Adobe ID (by using your email address).
Once ADE is installed you plug in your EZReader and have ADE authorise that device (keep in mind you can authorise up to 6 devices with one ADE ID).
I havent used Overdrive, but other epubs I have bought I have downloaded the file (.acm I think the extension is) and then opened that file up in ADE, which will then download the actual book you purchased.
From there through ADE just drag'n drop the file in the ADE window from your library to your EZReader.
Hope this is of some help.