Reference more for myself than for y'all, but you get the shared benefit.
To ship the logs from RHEL6 or Centos 6 to a remote syslog server, edit the following file: /etc/rsyslog.conf
At the bottom of the file, remove the comment from the remote-host entry, and update with your server name or IP. Example:
Restart the rsyslog service:
service rsyslog restart
Make sure you are receiving the logs at your syslog server.