You can give ads in news paper or in internet also. There are many free classified sites. You just give your details and describe yourself as a very good baby sitter. So that people can easily contact you.
You can advertise free on classified ad site. There you can post your advertise free on right section with details of your advertise. Its no need to pay there. There are lot of visitor to attract your offer there. they can see your advertise and come back to you. If you give your contact details, someone can contact to you.
PlanetAdvert
care.com
my parents don't have any friends that have young kids and I don't live in a neighborhood with young kids. how can I advertise that I am a baby sitter? and where can I put up fliers or something?