I need to understand how "su" works.

I logged into my server via ssh using an ordinary account - reg_user.

To become root, I then issue the command:

[reg_user@my_ip_address ~]$ su

This asked me for a password, which I provided. Now prompt changed to:

[root@my_ip_address reg_user]#

Because of the # sign, I'm assuming at this point that I've become root.

Well, when Issue a command such as:

[root@my_ip_address reg_user]# service iptables start

I get the error:
bash: service: command not found

However, when I login to via ssh directly as root, the command works fine.

What am I doing wrong?

Try using one of the following commands:
From the su man page:

Your $PATH is wrong. Do as the above poster said.

Thank you. su - worked fine.