You need to get an app from the app store that will allow you to (1) set up an Adobe Digital Editions (ADE) reader account and (2) access library books.
Two such apps come to my mind: Overdrive and Bluefire Reader. Both are free in the app store. Overdrive is specifically designed to [only] interact with it's library lending system, while Bluefire reader can do more. Both are great apps and since they are free ... why not get both?
Once you've got the app loaded and you open it, you'll be prompted to create an Adobe Reader account. This is the account you'll need to read library books (as they are "protected" with digital rights management, or DRM). Follow the prompts and establish an Adobe account. Then, you can download library books to your iPad.
Hope this helps. Give a shout if you need more info.
Marilyn