Keypair generation result

Forgive me if this is the wrong place to ask this question.

I have the task of teaching someone how to create ssh keypairs and, although I'm well versed in Mac OS X (currently using 10.5.5), I'm not much more than a novice in the command line. I've followed the advice at
and all went as suggested, except, I assumed the result of doing it would be that next time I used ssh to log into the remote Mac, I wouldn't be asked for a password, but I'm still being asked for it.

Are the guidelines on that site wrong? Am I expecting the wrong result?

Any pointers gratefully received.