Okay I found it and did what you said. That sounds like a weird way to allow passwords to be filled in on websites. I don't know what that has to do with sleep or screen savers.
Thanks for your help. Let's hope it works.
You turn on the screen lock by checking the box for "Require password [some time] after sleep or screen saver begins".
The padlock needs to be unlocked to make most changes on this pane, but (at least on Mavericks) the "require password" setting can be changed even if the padlock is locked.
