Step 1:
jsmith@local-host$ [Note: You are on local-host here]
jsmith@local-host$ ssh-keygen
Generating public/private rsa key pair.
Enter file in which to save the key (/home/jsmith/.ssh/id_rsa):[Enter key]
Enter passphrase (empty for no passphrase): [Press enter key]
Enter same passphrase again: [Pess enter key]
Your identification has been saved in /home/jsmith/.ssh/id_rsa.
Your public key has been saved in /home/jsmith/.ssh/id_rsa.pub.
The key fingerprint is:
33:b3:fe:af:95:95:18:11:31:d5:de:96:2f:f2:35:f9 jsmith@local-host
Step 2:
From Local-host, run this One liner for password less ssh connectivity.
cat ~/.ssh/id_dsa.pub | ssh useronanotherserver@anotherservername 'cat >> ~/.ssh/authorized_keys'