An obvious way to find a sitter -- I would start by asking friends you know well if they have any sitter references to share. You might be surprised some folks are reluctant to give out names of their favorite sitters... seems silly and selfish to me, but good babysitters are apparently hot commoditites.
Once you've rounded up a few names here's what I would do. Before you actually have anyone come to babysit, ask each one to come by your home for a brief visit -- say 20-30 minutes. It's like an interview. Take that time to introduce your kiddos to the prospective sitter and just let them hang out together; watch how she interacts with them. I actually ruled out a potential sitter once by simply watching her for 5 minutes with my kids. She was just too timid for my little tornados and I could tell she would be overwhelmed by them. If the sitter is younger than driving age, you'll also get a chance to meet the girl's mom.
Good luck!