The below example, describe how to set up SSH password-less automatic login from server A to B with user user.
Create Authentication SSH-Keygen Keys on A
ssh-keygen -t rsa
Create .ssh Directory on B
ssh uesr@B mkdir -p .ssh
Upload Generated Public Keys to B
cat .ssh/id_rsa.pub | ssh user@B 'cat >> .ssh/authorized_keys'
Set Permissions on B
ssh user@B "chmod 700 .ssh; chmod 640 .ssh/authorized_keys"
Login from A to B without Password
ssh user@B