The answer from Randal Schwartz almost helped me all the way. I have a different username on the server, so I had to add the User keyword to my file:
Host friendly-name
HostName long.and.cumbersome.server.name
IdentityFile ~/.ssh/private_ssh_file
User username-on-remote-machine
Now you can connect using the friendly-name:
ssh friendly-name
More keywords can be found on the OpenSSH man page. NOTE: Some of the keywords listed might already be present in your /etc/ssh/ssh_config file.