Probably the most efficient way to wash dishes, hands down, is the bucket method. (one sink of warm, soapy water, one sink of clean, water) with very few dishes!
But if you’re like most families the dishwasher is the way to go. Cut down on your dishwasher energy by doing the following:
Only run the dishwasher when it’s fully loaded.
Place cups between prongs, not on top of them.
Set the dishwasher to the “light” wash cycle.
Load it the smart way by placing the soiled side of the dish towards the center of the machine for better spray exposure.
Skip the dry heat cycle which wastes electricity. Just open the door and let the dishes air dry plus add moisture to your kitchen if needed.