Tablets usually don't show up in ADE (unlike dedicated ereader devices).
You authorize the tablet via whichever Adobe DRM compatible ereader app you are running on the tablet.
I suggest Bluefire, also consider Aldiko or Overdrive, or the tablet may have one pre-installed.
If you need to you can copy books to the tablet from Windows using Windows Explorer, the tablet should show up as a mounted drive.
Or you can copy them using something like Dropbox.
You should then be able to read them on the tablet.
As a tablet is more powerful than a dedicated ereader, you can probably buy/borrow books directly on the tablet and avoid ADE completely if you prefer.
You can indeed have up to 6 devices (including computers ruinning ADE) authorized with any Adobe account/ID.
I cannot copy the files to the ereader without using ade because of the way the library works.
Thank you! I had no idea I needed an app to add books. I downloaded overdrive, it asked me to add my library, I did so. I logged in, authorized my nook, and got my book! Yay!!