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.
The files I am trying to move to my Nook are .ascm files, and it says those have to be opened in ADE first then transfered. I will also look into the apps and see if those work.
You certainly have to convert .acsm files before transferring them to dedicated ereaders.
Converting is actually getting a book DRM book file (.epub/.pdf); the .acsm is just a token of purchace/loan.
It is probably best to convert them first even for a tablet,
but some tablet apps will be able to convert (as long as they have internet connection).
If you use Overdrive on the tablet it should be able to perform the complete borrow/download/convert/read process without using a computer at all.