The very best way to become acquainted with a great babysitter is through a referral. Your first phone calls should be to friends or neighbors with young children. Ask them who they use and if they'd be willing to share her name and number. If you don't know your neighbors, get gutsy and stop mothers in your local grocery store, kids' clothing store, or at the playground and say, "I'm sorry to bother you, but I'm new in town (or just had a baby) and I'm looking for a good babysitter. I was wondering if you could possibly help me out and recommend one?" Most moms have been in the same situation and will share their sitters.
If you're not bold enough to accost strangers, try calling the youth director of a large church or synagogue in your area for a recommendation. Also, many high schools and YMCA facilities offer babysitter certification courses and can give you the names of recent graduates. Some larger neighborhoods even run babysitting co-ops, where you trade babysitting duties with other mothers with children of similar ages.
Consider an internet search site, such as sittercity.com, which allows you to search for babysitters in your area and prescreen candidates.