This page has instructions on how to get started with passwordless login to remote servers over SSH.
You will need to generate a pair of keys on your local machine and then copy the public key to the remote machine.
Basically, you want to check if there are existing keys:
$ ls -al ~/.ssh
If you don't have keys there, you will need to generate some.
A problem that I was running into was that Ubuntu would keep prompting me to enter my key passphrase every time, which defeated one of the reasons for passwordless login.
The messages looked like:
Enter passphrase for key '/home/username/.ssh/id_dsa':
To get rid of the password prompt on each login, type
ssh-add and enter your passwords for the last time.