There have been many problems about the installation of the php-zip module. Since Mid of 2006 the php-zip module does not require the zziplib anymore - it uses its own implementation (which is a clean approach in a double sense - there are no source code comments). So, the following might possibly be only relevant for older installations.
Chris Branch has been kind enough to jot down the points of a successful php-zip installation sending it to me in May 2006. I am quoting his text verbatim - again, I do not know whether it works or not as I am not using any PHP for real work.
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Software Packages ** Apache 2.4.21 (Linux) ** PHP 4.3.9 ** ZZIPLIB 0.10.82 ** Special requirement: static linking
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Setting up ZZIPLIB ** Extract files from zziplib-0.10.82.tar.bz2 to a new folder. ** ./configure --enable-static ** make ** make install
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Rebuilding PHP to include ZIP support ** Modify PHP build file and add "--with-zip" [no dir needed because default /usr/local on my machine] ** make ** make install
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Modifying the Apache Installation ** Change to Apache source code directory ** Change to "src" subdirectory and edit existing Makefile. [-1-]
Add: EXTRA_LIBS=/usr/local/lib/libzzip.a ** Change back to parent folder (cd ..) ** make ** /usr/local/etc/httpd/bin/apachectl stop ** make install ** /usr/local/etc/httpd/bin/apachectl start
[-1-] Note: That step is the critical step that's not obvious. Apparently, when you build PHP as a static library and include the "--with-zip" option, it creates a static library for PHP with an external dependency on zziplib.a. However, the Apache configure script and resulting Makefile doesn't take this into account, so Apache won't link unless you hand-edit the Apache Makefile. (Maybe there's a better place to make this change so that you don't have to re-fix Apache's Makefile each time you run Apache's ./configure. However, I didn't spend the time to investigate that).