This has been covered in many places, so this will be a short version. This is not using the insecure r?? commands with .rhosts.
Assume both machines have the same or similar ssh installation.
"hosthere" is where you are logged on. "hostfar" is where you want to log on.
Use an empty passphrase and default key location.
hosthere $ ssh-keygen -t dsa
Place "pub" file on hostfar in ~/.ssh as "authorized_keys2".
hosthere $ scp id_dsa.pub hostfar:.ssh/authorized_keys2
Now ssh and scp to "hostfar" should not prompt for a password.
Troubleshooting includes checking permissions of .ssh directory and files.