This if simple and a great asset if you are trying to do automatic backups with rsync or anything else where you need unattended backups or login. This is for Ubuntu Distributions of Linux:
1) Generate RSA Key
ssh-keygen -t rsa
2) Copy the key to the computer you wish to login to automatically without a password:
sudo scp ~/.ssh/id_rsa.pub USERNAME@IP:~/.ssh/authorized_keys
(replace your username and IP address with your correct info)
That’s it! Now you should be able to use SSH and not have to enter a password to login.