1999 Dodge Neon Engine Coolant Drains as you put it in

I drive a 1999 Dodge Neon. While driving home recently, my car began to slowly overheat. Within 5 minutes there was steam coming from the hood, and the car shut off. I tried adding Antifreeze but the reservoir is empty within seconds. Im not sure where it is leaking but it seems to be coming out somewhere close to the reservoir. Is this something I should fix myself, and if not, how much would it cost to have it fixxed?