Adobe Digital Editions 2.0 does not generally recognize tablets, only dedicated ereaders.
For a tablet, install compatible Adobe DRM ereader app. I suggest Bluefire; also consider Akdiko or Overdrive but some people have issues registering them. Some tablets come with such an app preinstalled. Authorize the tablet from within the app to use your Adobe ID (details vary from app to app, usually somewhere within Settings)
The tablet may well be able to download books without use of ADE at all. If you do want to transfer books from ADE/computer, use a file manager (Windows Explorer, Mac Finder) to copy to the tablet as mounted drive, or use a utility such as Dropbox.