How do I archive my kindle books on my I pad?

There should be an "i" somewhere on the screen that will provide additional help.

With iBooks all that you need to do is hold the book image in the library and delete, stays in your purchased space with the bookstore.

With Nook reader, in the library you can touch on the top of the screen to pull down a list of operations that includes archiving books.

Kindle should have a similar function, though I don't normally use Kindle.

To delete a book from the Kindle, you tap and hold on the book in the list, then tap the x in the upper left corner when it appears. You'll be able to download it from the archive later if you want.