When you want to use these computers from the outside connect
with ssh to the server
That computer also has shorter aliases you can use, like
(If you work here and have one of these computers in your room you can preferably connect to that one instead. Also if you are sitting in one of the computer rooms with a laptop you can connect to the one you have right in front of you. But most of the time avoid connecting to those computers. If someone sits down at that computer they are supposed to have it for themselves.)
If you have a Unix compatible system like GNU/Linux you will have ssh on it. You can run it as
ssh -Y firstname.lastname@example.org
For graphical programs that create windows to work you need to have
X.Org X Window System (or equivalent) running on your computer.
With GNU/Linux you will have that. With macOS take a look at
But if you run a Microsoft OS you probably don't have ssh on it. One way then is to use Putty.
That gives you a terminal window. To run programs that show windows the most common server to use is Xming X Server for Windows.