Build and run Apache, MySql, PHP from source 
for a user account without root permission:

Create a directory, say sources. Then: 

  cd sources
  cp .../userlamp-makefile .
  tar zxf .../httpd-x.y.z.tar.gz
  tar zxf .../mysql-x.y.z.tar.gz
  tar zxf .../php-x.y.z.tar.gz

  mkdir -p $(HOME)/servers
  make -f userlamp-makefile

This will show you the build and run steps. 
Follow the steps.