I can't say what's actually required, but since the library authors were awesome enough to release with such a liberal license you generally can't go wrong as long as you make an honest effort to try to credit them.  Here's what I've seen:

- A copy of the GPL in its own file at the top level of the source tree.

- Copyright and GPL notices at the top of each source file that you write.

- Note in the readme what zlib libraries you used, who authored them, and provide a link to each one.

- Any libraries go in a separate directory in your source tree, and when possible leave them exactly as you obtained them (i.e. leave their readme or license files in there).

- If you make any changes to the library, be sure to make that as obvious as possible, maybe a note in the top level readme and the library readme, or maybe even a separate text file in the library folder.

If you want to release your code under the GPL, you'd generally include a copy of the GPL under then name 'COPYING' and add a small note at the beginning of all your source files. For zlib/libpng licensed code, you don't really need a separate license file, because the complete license usually is distributed at the beginning of each source file.

But all of the above is just a formality, anyway.  You can just put a file up somewhere and say "this is released under GPLv3 as published by the Free Software Foundation", and that's enough, legally speaking.

the FSF actually has a very nice pag about how to do this:

http://www.gnu.org/licenses/gpl-howto.html

I recommend following its recommendations :)