First, you should follow this guide: http://wiki.rubyonrails.org/rails/pages/RailsOnCentos to install Rails and Ruby in general.
After you install RubyGems, install passenger by issuing gem install passenger.
After the installation completes, issue: passenger-install-apache2-module at the command prompt.
The installation steps should be straightforward, and it’ll tell you how to work through everything.
If you get the following error: cannot open /httpd/build/config_vars.mk: No such file or directory at /usr/sbin/apxs line 201 (this may appear at the beginning of running passenger-install-apache2-module), you need to install apr-devel. Issue yum install apr-devel to take care of that.