In order to set up rsync to work without a password, you first need to make sure that you can do so with a password:

rsync /local/path username@/remote/path

If successful, then generate a public/private key pair, but be sure not to give a password:

$ ssh-keygen
Enter passphrase (empty for no passphrase):
Enter same passphrase again:

Then copy the public key to the remote host — note that ssh-copy-id will copy the file to the correct location for you:

ssh-copy-id -i ~/.ssh/id_rsa.pub username@/remote

Make sure that you can ssh without a password:

ssh jlaudun@/remote

Now try rsync adding the argument -e ssh to specify the remote shell to use:

rsync -avz -e ssh /local/path username@/remote/path