Oil burning

There are really only two likely ways for oil to get into the cylinder. Up from the bottom through worn piston rings, or from the top via damaged or worn valve seals. If the car has good compression the seals are the likely cause. The "why" is a little more complex. Heat, poor oil change intervals, rough driving, long periods of sitting, a life of very easy driving, foreign debris, or acts of God could all play a roll in either condition. Without knowing what is actually wrong, it's tough to venture a guess toward the cause. How is the rest of the car? It it's in great shape it might be worth fixing any way. If it's falling apart, you might be better off to make it last as long as possible as-is.