I'm trying to install mod_pagespeed for Apache server, but I can find instructions only for Linux. Is there any tutorial or description on how to do it on Mac?
Instead of using apt-get you can install brew. Brew is a lightweight package manager for OS X and can be obtained at their official homepage.
I'd recommend to install a Linux distro on a VM and then installing mod_pagespeed as this is way easier, plus you get more support probably.