Hello! I'm not sure if you want to start a babysitting business (where you assign lots of babysitters to jobs), or if you are wondering how to find babysitting jobs. This answer is for finding babysitting jobs.
Trust is super important to babysitting. Parents will only let you look after their kids if they trust you. A good way to build trust is to provide references to parents. References are the names and phone numbers (or emails) of 2-3 parents you have babysat for before, who are willing for other parents to call or email them, and who will speak very highly of you to these other parents.
A second question is how do you figure out which parents need babysitting for their kids. One way to do this is through your own family/friend network--who do you know that's looking for childcare services? Another way is to join sites that are gateways of babysitters. You can register as a babysitter, complete a profile, and wait for jobs to come to you. On these sites, it's very important you are honest in the information you provide and do a good job of filling out your profile. These sites include: