Moving this discussion to the Adobe Digital Editions forum.
Please see View e-books | iOS, Android devices -http://helpx.adobe.com/digital-editions/kb/view-e-books-ios-android.html for information on how to locate a compatible application to utilize on your iPad.
Digital Editions (ADE) does not run on the iPad.
You can use an app such as Bluefire to read DRM or non-DRM eBooks.
Register it with the same AdobeID as you use on your PC/Mac.
You can then copy .epub files from the PC/Mac and open them in Bluefire.
(I think you can copy the .acsm files instead, and Bluefire will then download the .epub files)
Apple likes to make this copy process awkward: three ways that work are  iTunes.  Dropbox,  email to yourself.
Choose whichever suits your way of work best.
As far as I am aware there is no way using ADE.
If you use Dropbox, it will at first say that it cannot open the file.
However, there is a dropdown icon at the top right that should give the option to open in Bluefire.
If you want to access library books directly on the iPad, there is an Overdrive app for iPad.
Also, some companies (such as Barnes and Noble) have their own apps to allow books to be gought/read directly on the iPad.