As for actually finding the babysitter, put an ad in the classified section of the paper, or post flyers at a nearby college (I saw tons of flyers at my college year round looking for babysitters)
My friend just accepted a Live-in Nanny position, she just graduated from college and is wanting to work a year or two before applying to grad school -- she found the family/they found her through the website:
www.greatnannies.com There is also
www.enannysource.com You don't have to pay anything to make a profile, and You don't have to pay the website when you find a match.
You can set up a profile both as a "nanny" and as a "family" and post what you are looking for -- i.e. full time, part time, occasional, what hours, etc.
You can set up an interview with the person and ask for references from families the prospective babysitter has watched before.