Best ask in the Adobe Digital Editions forum.
You must use an app such as Bluefire of Aldiko (for general use, including library books),
or Overdrive (for library books)
Quite a few people have authorization issues with Overdrive.
When working right, it should be able to borrow, download and read library books with no intervention from a computer.
With Bluefire and Aldiko you generally need to get any DRM books first on ADE on a computer,
then transfer the .epub file to the tablet using a file manager such as Windows Explorer or Finder.