Wash dishes only when you have full loads. Learn how to properly load your dishwasher – the more dishes you can properly fit, the less times you have to run it (Good Housekeeping article for some tips). Also, scrape off the food scraps instead of rinsing each dish before you load it. 

By purchasing ENERGY STAR-rated appliances you can save water; approximately 5–15 gallons per dishwasher load and approximately 15–45 gallons per load for washer.

Washing by hand? Kitchen faucets can spew about 2 to 5 gallons of water per minute. If you're letting your faucet run the entire time while you're washing dishes, you've already used the same amount of water as a dishwasher after approximately 2 minutes.  Instead of letting the water run, fill the sink no more than half full with water and detergent, turn off the tap, and wash a stack of dishes at a time. Don't drain or refill the sink unless the water becomes cold or dirty. Rinse your dishes in standing water.