Hi
If all you want to do is control one mac from your mac you don't need ARD. VNC (Screen Sharing/Remote Management) is built into every mac. As such all you need do is make sure either of those services have been enabled (Sharing Preference Pane) and you've opened up the relevant ports (5900, 3283) on your friend's router/firewall to forward remote traffic to his assigned private IP address.
From there it gets a bit tricky as two things may happen which could limit how effective this all is as well as potentially confuse you both:
(a) the external IP address (assuming a residential broadband service) assigned to your friend's router may change over time.
(b) the internal IP address assigned by your friend's router may also change over time depending on how many devices are connected at any one time on his/her private network.
If you and/or your friend are farmiliar with some of the basic concepts of IP addressing, routing, port forwarding and router/firewalls you may have a chance. If neither of you have any idea or find it too complicated you could instead try iChat Screen Sharing (free) and/or LogMein (free). It's been a while but I think Skype also offers a screen sharing/control faciliy?
HTH?
Tony