Normally what I do is create a key on my remote system, like so:
If you want no-password, don't specify a passcode here; though it's fair to warn that this is considered bad security by the people who consider such things.
Next, I copy it up to my (password-enabled) ssh server:
ssh-copy-id -i ~/.ssh/id_rsa.pub someremoteserver
After that's done, you should be able to login via ssh from that specific device (or any other device to which you've copied id_rsa.pub) without a password.
Now you lock down ssh so that it doesn't accept passwords. In /etc/ssh/sshd_config on the server:
Restart ssh and you're done. This is no way affects the way local console logins work; they'll continue to accept passwords as normal.