Dental services for low income families are available in most places with the possible exception of the most rural areas. It will take a little research but almost anyone can find free or low-cost dental care.
Start by calling your local Department of Human Services. Even if you do not qualify for Medicaid, they will be able to give you a list of clinics for sliding scale medical and dental care based on income. Some of these provide free services or services with a very small co-pay of five or ten dollars.
If you live near a university that has a medical school they will often have a dental clinic that is staffed by the dentists who teach at the university and their upper-division students. Students will be supervised by experienced dentists and can do exams, cleanings, x-rays and other basic services while the experienced professors will do more complicated procedures like root canals and extractions giving students the opportunity to watch and learn. Naturally, one of the quickest and easiest ways to find information on free care is to go to the web site of the American Dental Association. Most libraries have computers available to the public, and the ADA website has a search box in which you can type "free dental care" to get a list of free and low-cost dental clinics in your area. That same website will also have a list of dental schools throughout the United States that provide free or reduced-fee services.
Another website with a lot of great information is www.freemedicalcamps.com, and there, you can find not only places for free and reduced-fee dental services, but also low-cost medical care as well. You will have to do some digging because there is a lot of information to go through but with a little patience, you should be able to find a place to help.
Finally, some church groups run subsidized medical and dental clinics for uninsured and low-income community members. Going through the local phone book under "Clinics" may help, or a call to the Salvation Army, Catholic Charities, or any local church can get you some names of places that serve the low-income public. There is help out there, and a little patience and research should be enough to provide the help you need.