In theory it's simple: She (the best babysitter) should simply be just like you. You know (what mother wouldn't?) what's best for your child, you know how to handle any possible given situation, and you know just how careful you have to be while performing certain tasks. The problem is, there is (currently) only one of you. So how do you determine who is the next best option?
Consider what are the things that are important to you as a mother. Firstly, it has to be someone who really cares. Someone for whom being a babysitter is not just a job, but a passion. Even if you have to teach someone from scratch, she will eventually be able to become a good babysitter, because on top of everything she is taught, she cares. Someone who really cares will have a gentle manner, and an ever watchful eye. Exactly what you want.
Secondly you are looking for someone with some experience. Some things are only learned by doing them, so experience is a definite advantage. Someone having some experience will also have contactable references, so you can get some more background information.
Next up is knowledge. Does she know how to cook, or at least slap up a meal, and (if applicable) does she know how to prepare the baby's formula? Does she at least have a basic knowledge of first aid, so she can respond (and not panic) if something unexpected happens?
The best babysitter is someone who will deal with any given task or situation as you would. She doesn't have to be the best when she starts working for you, but she has to be willing to learn, and follow instructions. When doing the interview, trust your instincts: They're usually right.