Could somebody please explain the document libraries to me. There are
multiple document libraries in the new version. I noticed that for each
categories/topics there is a document library. But the question is, how
do I navigate to them without having to type in the URL?

Also under My Site, I uploaded a document into a Shared Document
Library. Somehow the document ended up under the document library for
Operations. Why?

And why is it that when I do a search for this document, I don't get a
result?