How do I go about filing for child support if the father is in the army and is about to be deployed?

First, you could try contacting the military unit and make a claim for support with them. You can also go to your local county child support services agency and open a case for child support. They should handle the rest but it may take awhile. With respect to a court action, an attorney would have to evaluate your specific case to determine if the State where you live has jurisdiction to make a child support order.