Well, to be “correct” the title of this should have been “how to add your key to the list of authorized public keys on a remote or local linux machine”, but being a newbie like myself, I would not have known to search for it. If I wanted to find out about logging in automatically to a remote machine using a generated public key, I myself would have used “Passwordless SSH” – so there you go.
To get started, I’ll assume that you have OpenSSH set up (it’s setup by default… well usually) and that your remote machine has OpenSSH-server set up.
If not, then do the following on the remote machine:
$ sudo aptitude install openssh-server