Average clothes washer uses 40 gallons of water per cycle.  Its energy use will depend on the cycle’s water temperature.  The hotter the temperature, the more energy it will use.  The mechanical operation of washer itself does not consume a lot of energy.

You can find out how much power your washer uses by checking out Find Energy Use by Appliance. So here are some tips:

• Choose a cycle with cold rinse, rather than warm or hot rinse.  It is not the “washing” part that takes a lot of water, it is the “rinsing” part.  So washing in hot or warm water won’t consume nearly as much energy as rinsing in hot or warm water.
• Choose a cycle with automatic temperature sensor.  This way the washer will use appropriate amount of cold water to accommodate for the required temperature setting, potentially saving energy on hot water use.
• Try to maximize clothes load every time you use a laundry machine.