Is that a kobo tablet, or dedicated ereader?
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For a tablet ...
For Overdrive library books, you can install the Overdrive app on the Kobo.
That should allow you to borrow, download and read library books on the Nook without using PC/Mac/ADE at all.
For other books you may need to install ADE on a computer; register it with your Adobe ID and use it to access and download books.
There are then various DRM eBook apps that should work on the Kobo.
Try either Bluefire Reader ( http://www.bluefirereader.com/ ) or Aldiko ( http://www.aldiko.com/ )
Register it with the same Adobe ID as you use on the laptop.
Copy books from the computer with the Kobo plugged in, using a file manager such as Windows Explorer or Finder.
You should then be able to read them on the Kobo.
I'm not sure if the Kobo comes with an Adobe DRM capable eReader app builtin.
Also not sure if any of the apps will integrate with ADE to allow copying direct from ADE (as with a dedicated eReader) rather than using file manager.
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For an eReader ...
There are bugs in ADE2.0 that prevent it recognizing some eReaders.
Try to see if the older but more reliable v1.7.2 works.
Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
http://helpx.adobe.com/digital-editions/kb/cant-install-digital-editio ns.html
The forum software is sometimes corrupting the link above. There shouldn't be a blank in 'editio ns.html'. The following redirects to the same page: http://tinyurl.com/diged172