Welcome to the forums, Dallacruiser. Fret no more - we're here to help
Adobe Digital Editions is software you install on your PC to read ebooks in PDF & EPUB format. Your Pocket eDGe already has the equivalent software installed on the Reader side - there's nothing you need to install

You don't need to use Adobe Digital Editions for library books.
If I understood the
article about borrowing public library books, you run the Overdrive application on your PC/Mac to select and check out a book. When you download it, you select "Save File". At this point, I would plug a USB memory stick into your PC and then save the EPUB/PDF file there. Once it's downloaded, you can unplug the USB memory key and plug it into your eDGe.
Then, on your eDGe, launch the "Storage" application and tap "USB0". There you'll see the book you downloaded. Tap on it to open it up on the Reader.
If you're using an Overdrive application on your eDGe, then it will be storing the downloaded ebook somewhere. If this is the case, I'll have to find out where it stores it so I can tell you how to open it on the Reader side.
I don't have access to a public library that uses the Overdrive system, so I'm going on my understanding of the previously mentioned article and reading ebooks on the eDGe in general.
So, please ask further questions if necessary and describe in detail what you tried, including which app you used on which device (i.e. PC/Mac/eDGe)