Finding the page number of the last page of a document, from within the document, is somewhat tricky. The lastpage and zref-lastpage packages define a label LastPage whose number is right (after sufficiently many passes through LaTeX, of course). The memoir class also defines a “last page” label.
The documentation of the fancyhdr package spells out exactly how one might actually use this information to produce page numbering as suggested in the question.
This answer last edited: 2012-10-16