If you don't see signs of a leak outside the engine, first check the oil level. If it's normal, that's good because coolant will melt the first layer of the engine bearings. The most common cause of unexplained coolant loss is a leaking cylinder head gasket. There's two tests to verify that. One is done by your mechanic. He will draw air from the radiator or reservoir through a glass cylinder with two chambers partially-filled with a special dark blue liquid while the engine is running. If coolant can leak into the combustion chamber, usually combustion gases can also leak the other way into the cooling system. That will make that dark blue liquid turn bright yellow.

If the leak is too small to show up that way or if the coolant is leaking slowly somewhere else, you can add a small bottle of dark purple dye to the reservoir, drive it a few days, then search with a black light. The dye will show up as a bright yellow stain that you can follow back to the source. Check all around the engine and radiator, and at the tail pipe.