I check library books out in the mobipocket format and read them just fine on my Cybook, once I made the simple change discussed in
this thread. I have left my Cybook for several days and never had a problem picking it back up and reading the library books as long as the books have not reached their expiration dates. There must be some kind of date function in the Cybook software because the software keeps track of the books' expiration dates.
All you'll need to do is register the Cybook's PID with the library (there's probably a page on your library's website where you'd do this), and then you can download the books to your computer and then transfer them to the Cybook. If you are running the latest version of Firmware, you may not need to perform the fix described in the above referenced thread.
The only time I download books to the Overdrive software I've installed to my computer is if I check out an audio book. When I checkout audio books, I download them to my computer and then use Overdrive to sync the books to my Zune.
If you run into problems, leave me a private message or post in this thread and I'll try to help you work it out.