ngine burning oil

I believe my Saturn S series (2001) is burning oil. Only a week or two after an oil change, it is completely empty. When I first start the car, there is a bluish smoke emitting from the tailpipe. I had another car with the same problem. It was burning oil. Two large chain car repair shops stated I needed to purchase another engine (very expensive). Is there another option? Can the "burning" be repaired? What is happening when a car burns oil?