First, what type of books are these? Adobe Digital Editions (ADE) books are not in any particular format; ADE describes the method by which you read them. As in, you open the Adobe Digital Editions reader to access the books. They can be in many formats: e-pub, PDF, mobi, etc. The key here is if they have Digital Rights Management (DRM) attached to them.
If they don't have DRM, you can simply move the e-books over to your iPad with iTunes, or e-mail them to yourself, etc. Then, you can use "Open In" to pick an e-reader app to read them with.
If they are from a public library, they have DRM and you can download an app called Overdrive. You can access the library through this app, checkout/download a library book and start reading.
If you got them from a major book store, they probably also have DRM and most have their own apps (Kobo, Borders, etc.). You should be able to access the books via the apps themselves.
If all else fails, you can use the app Bluefire Reader, which will allow you to read DRM books.
If I've gone way off base in regards to your question, or if this doesn't make sense, let me know. Else, good luck and happy reading.
Marilyn