You meet through an online dating service, get married and soon you’re going to an online babysitter service such as sittercity.com, 4sitters.com and babysitters.com.
Each operates much like a Web dating service, in that the host site doesn’t legally vouch for its registered sitters. Sittercity requires a reference from each sitter, and it allows the posting of eBay-style feedback, but it does not, for example, conduct criminal background checks.
Parents and negotiate rates, which typically run from $10 to $15 an hour. I don’t know how that compares to rates charged by the typical teenage girl down the street, assuming such girls still exist.