Copying your public key (usually
~/.ssh/id_rsa.pub) to your remote server makes it possible to login over ssh without needing to remember your password. All the authentication is taken care of between the remote machine and your local one using private/public keys.
On your local machine simply run the following command on one line in a terminal
cat ~/.ssh/id_rsa.pub | ssh firstname.lastname@example.org "cat >> .ssh/authorized_keys"