That is the problem of every single parent who does not live close to a loving grandparent. Finding a good babysitter is like finding a treasure.
My daughter wanted to babysit this year. She had done some babysitting during high school. I told her to make sure she took a CPR course and also a first aid course.
She did this and then registered with Sittercity.com. Soon she got a position working for a lovely family and absolutely adores their two little boys. The family even took her along while going on vacation this summer to Disneyland.
There are not many companies I can personally vouch for that I post advertising for but this is one that I can say is excellent.