Typically a well pump fills a pressure tank. By knowing the max and min fill levels of the pressure tank and how often it cycles, you would roughly know consumption. The measurement would be off by the amount used when the pump was running, but it would get you close.
To measure the difference between min and max fill, turn off all water use in the house except for a bath tub faucet or a place you can fill a five gallon bucket. Turn on the water until the pump starts then turn the water off. Wait until the pump is finished then begin filling and emptying a 5 gallon bucket until the pump starts again. Counting the number of buckets gives you the volume difference.
You could also try to determine the flow rate of your pump, but since the flow rate is pressure dependent, it may give you a less accurate answer unless you put a pressure transducer in the line and calibrated.
There are a variety of ways you could count the pump start up/ durration. It really depends on your skill set as to which one is easier. An arduino, raspberry pi, or PC with a daq or other inputs would all work well. A relay to the pressure switch would work, but a little dangerous and unnecessary. A split core current sensor is a nice solution that can also tell you when there are issues with your pump. You could also do it simply with a well placed microphone. You could use a python library on the PC with standard audio input or a pre-made board for arduino or rpi.
