Step 1
As the user you are going to be running rsync as, and on the machine you will be running rsync on, type: ssh-keygen -t rsa
Follow the prompts and use the defaults for the filenames it gives you. Don't enter in a passphrase, otherwise you will still be prompted for a password when trying to connect.
You should then have two new files in ~/.ssh, id_rsa and id_rsa.pub.
Step 2
Open ~/.ssh/id_rsa.pub and copy the line in it to the ~/.ssh/authorized_keys file on the host you will be connecting to as the user you will be logging in as.
Step 3
Now try it out. Try ssh'ing from the host you created the id_rsa* files on to the one you added a line to the authorized_keys file. You won't be prompted for a password any more.