This post is intended mainly to Zyxel NSA310 users.

Prerequisites
See first https://adrhc.go.ro/blog/common-commands-when-building/ for building environment, x.sh script and other things not defined here.
Before starting do declare the environment variables specified to the link above.

Environment & other preparations
NEW_BUILD_NAME=ngx_pagespeed
NEW_BUILD_VER=20150317
NEW_BUILD_NAME_AND_VER=$NEW_BUILD_NAME-$NEW_BUILD_VER
ls -l /tmp/$NEW_BUILD_NAME-*
ls -l ~/ffp_0.7_armv5/packages/$NEW_BUILD_NAME-*
NEW_BUILD_NR=0

wget -O ngx_pagespeed-$NEW_BUILD_VER.zip https://github.com/pagespeed/ngx_pagespeed/archive/master.zip
unzip ngx_pagespeed-$NEW_BUILD_VER.zip
mv ngx_pagespeed-master/ ngx_pagespeed-$NEW_BUILD_VER

Build procedure
Read then do first https://adrhc.go.ro/blog/install-configure-googles-mod_pagespeed-for-apache/
cd ~/compile/mod_pagespeed/src/net/instaweb/automatic
~/x.sh ffpg1
make BUILDTYPE=Release AR.host="$PWD/../../../build/wrappers/ar.sh" AR.target="$PWD/../../../build/wrappers/ar.sh" all

Other considerations
See also https://github.com/pagespeed/ngx_pagespeed/wiki/Building-PSOL-From-Source