The last time I attempted to compile mod_gzip into Apache, I found that the instructions for doing so were not documented clearly on the project page. After a couple of failed attempts, I finally found the instructions buried at the end of the ChangeLog document.
I present the instructions here to preserve your sanity.
Before you can actually get mod_gzip to work, you have to uncomment it in the httpd.conf file module list (Apache 1.3.x) or add it to the module list (Apache 2.0.x).


Now there are two ways to build mod_gzip: statically compiled into Apache and a DSO-File for mod_so. If you want to compile it statically into Apache, just copy the source to Apache src/modules directory and there into a subdirectory named ‘gzip’. You can activate it via a parameter of the configure script.

	./configure --activate-module=src/modules/gzip/mod_gzip.a
	make
	make install
	

This will build a new Apache with mod_gzip statically built in.
The DSO-Version is much easier to build.

	make APXS=/path/to/apxs
	make install APXS=/path/to/apxs
	/path/to/apachectl graceful
	

The apxs script is normally located inside the bin directory of Apache.