You're smart to assess the need. You really need to see what the situation is where you live. Ask around among your friends, your neighbors--most people do NOT want to hire someone they do not know to come into their homes and companion their children. So your best bet is to find friends and family members who might be interested in contracting your services.

Now, I have a question? What do you bring to the job? Are you qualified/certified in first aid? Are you reliable? Are you educated in child development, child safety issues? What kinds of activities would you be bringing to entertain your charges? What experience have you had supervising children? Do you have a reliable car and clean driving record (in case of an emergency). How do you keep your head in an emergency, for that matter? These are all questions you might be asked by responsible parents looking for a babysitter. The better your answers, the better chance you'll get the job, and be invited back a second/third time to work for them.

My suggestion would be to get yourself a first aid certificate that shows you've been qualified. Then put together a bag of activities for various ages, to show the parents that you really understand the role of a babysitter. You might consider putting together a questionaire so you'd have all the necessary info (where will parents be? emergency numbers if you can't reach the parents, pediatrician/hosptal/ambulance numbers, etc)

The more prepared you show yourself to be, the more likely you'll get the job, and in some cases, the more you'll be able to charge.