First you need to generate a so-called RSA key. Type
ssh-keygen -t rsa
This will create two files: id_rsa and id_rsa.pub. The first should be kept secret, the second is public. You should now login into the remote machine. If the file ~/.ssh/authorized_keys exists, append the contents from the file id_rsa.pub to it. If it does not exist, create the directory ~/.ssh (with permissions rwx for yourself and no permissions for group and others) and the file authorized_keys (with permissions rw- for yourself and r-- for group and others) with as its contents the file id_rsa.pub.
You should now be able to do passwordless ssh logins.