I have a 25 year old Sears Kenmore 1068439511 19 cubic foot refrigerator. I know it's costing me a mint to run - how can I check on it's power consumption?

There should be a tag on the refrigerator that will tell you what your amperage usage is when the compressor is running. You can multiply the amperage by the voltage (115) and that will give you the wattage. This will tell you what your wattage is when the compressor is running. If it's frost free, you'll use some extra power when it goes into defrost, usually two or three times a day.