It took me years of living on my own to learn my parents were doing it wrong:

The dishwasher doesn’t need to be full to run it. You can chuck everything in after a meal and start it immediately.

Detergent and water are cheap, and even if it’s only a few dishes the machine uses less water than doing them by hand. Also, use liquid or powder detergent and make sure to fill the pre-wash detergent holder – detergent pods are a rip off.