Without know which app you are using - this is how it works in Pages.
When I use Pages on the iPad, I have to tap on the + sign in the documents window in order to create a new document. When I tap on the + sign - one of the options for the new document is "copy from iTunes". I select that option and then a window with all of the documents that appear in the Pages file sharing window in iTunes on my computer will pop up. I swipe down to the document that I want and select it. I can then import it as Pages, PDF or a Word file.
The point is, you probably have to create a document in whatever app you are using and use the copy from iTunes option.