What happens next?

How to convince a customer you are a responsible babysitter
Type up a resume and be prepared to give it to the customer upon your first meeting with them.
Include your past babysitting experience, if you are trained in cpr (most customers will be very happy to see this on a resume), and at least two reliable references.
Look neat and presentable at your first meeting with the parents.
Wear decent clothes, and make sure your hair is combed through. A fancy outfit is not necessary, just something that looks nice.