working on a remote Mac
There are many ways to achieve your goal. Apple has its own product: Apple Remote Desktop.

But in your case I would suggest another tool called Teamviewer. It is free for non-commercial use and easy to handle. Both sides (you and your friend) have to install the teamviewer application. When startet, you don't have to bother with IP adresses or whatsoever. Teamviewer will give you an ID and a password which is enough to connect to your friends mac.
It is platform indipendend and will work also on lots of Linux distributions.

Another nice, maybe even easier to use but non-free service is Gotoassist. This service does not need to install software on the remote machine. The remote machine just has to open a specific link in browser and you're done.

As I mentioned before, there are many other possibilities depending on the type of support one wants to offer, for example: SSH or VNC.