Hi. I am new to this. I have downloaded a book from my air ipad where do I find the download is it itunes or cloud am confdsed and where will my library be. Thanks

Where did you download it from and how ? If you downloaded it from the ibookstore in the iBooks app then it should be on the bookshelf back in the iBooks app (tap the Library button at the top left of the store if you are still in it). Only ibooks that you buy from the ibookstore or your computer's iTunes will show in the cloud for redownloading in the Purchased tab in the ibookstore in the iBooks app (and they will only show there whilst they remain in your country's store).

If you were using a site on Safari then unless you specified an app to download it into then it will only be in Safari's cache and will you won't be able to access it. If you did buy it via Safari then depending upon the site that you bought/downloaded it from then it might have digital rights management on it that will tie it to that store's apps/ereaders - if the site has its own app in the app store then download that and you might be able to download the book directly in it.

There is a FAQ for iBooks here : http://support.apple.com/kb/HT4059