Public/Private key authentication with SSH, passwordless

On the local server, logged in as, eg. myuser:
Change to myuser's home directory.

mkdir /home/myuser/.ssh
cd /home/myuser/.ssh
ssh-keygen -t rsa

NOTE: When asked for file in wich to save the key, make sure the path reads /home/myuser/.ssh/. We want to save the new generated key-pair in /home/myuser/.ssh/. Also make sure not to specify a passphrase, otherwise, you will still have to input a password at logon. You can also choose to generate a type DSA pair in place of the RSA key pair.

scp /home/myuser/.ssh/id_rsa.pub myuser@remote-server:/home/myuser/id_rsa.local-server.pub

On the remote server, you wish to log into:

mkdir /home/myuser/.ssh
chmod 700 /home/myuser/.ssh
cat /home/myuser/id_rsa.local-server.pub >> /home/myuser/.ssh/authorized_keys
chmod 644 /home/myuser/.ssh/authorized_keys