Downloading libraray books to iPad

Which library do you mean? The only app I'm aware of that works with public library offerings is Overdrive.

I'm guessing this would be what you are looking for

http://www.barnesandnoble.com/u/nook-for-iPad/379002216/

As Michael already said, Overdrive:
http://itunes.apple.com/us/app/overdrive-media-console/id366869252?mt=8

And for some libraries, those which have their content in some of Adobe's protected format, Bluefire Reader claims to work:

http://itunes.apple.com/us/app/bluefire-reader/id394275498?mt=8

I haven't tested it myself yet, though.

Regards.

I have just successfully used BlueFire to view books on my iPad. I had downloaded them from our public library on the iMac and had a bit of difficulty figuring out how to transfer them to the iPad. The file sharing instructions in iPad help didn't work so I tried emailing them to myself as attachments. When I clicked on the attachment, I was asked what app I wanted to use and voila readable files! I did of course have to first authorize the iPad with Adobe.

As a user of the Canadian iTunes store, I can't get the Barnes and Noble app.

I use overdrive and works great! Go to your local library website and see if they offer ebooks then see which program they use for it and look to see if theres an app for that program.