Log into a server using secure keys instead of typing a password

On the client:

1. ssh-keygen -t rsa
2. accept the default filename
3. press enter for a blank password
4. a private (id_rsa) and public key (id_rsa.pub) will be created
5. copy the public key to the server
   

On the server

1. cat id_rsa.pub >> ~/.ssh/authorized_keys
2. chmod 700 ~/.ssh
3. chmod 644 ~/.ssh/authorized_keys

Now back up your keys.

See also this and this.
(Upon error "Agent admitted failure to sign using the key", log out of the client and log back in again to fix).