To be honest, i've never hired a nanny. but i've considered it and gotten some information on how to hire one. It did have a list of things to do before and doing a background check was one of them, as well as getting refrences and actually speaking to the previous families. As far as doing the drug test, I'm not to sure about that. That might be going to far, but I think it would be suffiecent if you want to go take them for a physical and ask that doctor if he wouldn't mind doing a drug test as long as your nanny agrees as well. I think if you go to your local library or income tax preparer they can help you with that. I don't know how you would handle that.
Another way to do is to enroll them in an education center. I've looked into those a few times. They're not day cares, they're like a little school for toddlers! But some of them just say education center, you may want to visit a few times before you enroll to make sure they are doing a good job!