Keep an eye out in your area for signs posted at your local restaurants. Other ways this might be advertised is inside of the restaurants, on the menu, in newspapers or other advertisements or online through the restaurant's or other web sites.
Look for online resources where you can search for places in your area with kids eat free nights. These will tell you what offers are available on specific days of the week, etc. Some examples of websites you can use are:
Some nationwide chains currently offering kids eat free promotions are:
Another way to find free kids meal offers is to find out if the restaurants you frequent have a kids club you can sign up for. These normally offer free birthday meals or other discounts.
Be aware, if you find a national listing for a restaurant chain advertising kids eat free nights, it is up to each individual restaurant whether or not they want to participate. Always check first with the restaurants in your area. It is likely you will be required to purchase an adult meal to get the free kids meal. Check with each restaurant for their restrictions and requirements.
photo: polska1, sxc.hu