Do you have current daycare families? Are any of them on facebook? If so, ask them to like your page. When someone likes your page, that will show up in their friend's news feed (if they have it set that way) So when one of their friends sees that your daycare "mom" has liked "Tiny Twig's daycare" the friend now knows about you too.

I am new to Facebook too. I set up a personal account so I could have "friends" and I then made a separate page for my daycare. I don't really have any interest in the personal side, although I do like to see what others post, but I am really enjoying having the daycare page. I post pics of the kids and our activities almost every day. The parent seem to be enjoying it. I can invite my friends to like my business page. And because it is set up as a business page, it has different options than a personal page. I am still new to it so I don't know all the ins and outs yet but there is a feature called insights. Statistics about your posts, how many likes, shares, comments, where the people are who interact with your posts, and there are ways you can pay to advertise in the right places for your business. I have not gone that far, I'm not interested in paying facebook, but it can be done. I often have people whom I do not know like my daycare posts because they know the parents or kids in my daycare.