Q: I purchased several books last night on ibooks, and see them in my library, but I cannot figure out how to open them so that I can read any of them?

In iBooks on your iPad, when you seem them on your bookshelf, what happens when you just tap on one?  It should just open at that point.

That sounds like you are still tapping on the title in the book store, not in your iBook library.  Does the word "Library" appear in blue in the upper left?  If so, tap that, and if necessary, tap on collections and choose books, then tap on one of the title on the bookshelf there.

The word "Books" should appear at the center top, and the "Store" tab will be on the left now as you are now in your own device's downloaded content library.

You are welcome - enjoy your ebooks.  I have not bought an actual DT (dead tree) book in over two years now, but have hundreds of ebooks in my library.