Saving money on electricity is not about budgeting but about regularly checking that you are getting electricity at the lowest rate and doing everything you can to reduce the amount of electricity you use.
To really start saving money on electricity, get quotes from the electricity suppliers in your area and change to the one that offers the best deal. Check prices at least once a year on "What's my number?" and Powerswitch.
If you own your own home and live in a colder part of the country, installing insulation can pay for itself over a number of years. www.energywise.govt.nz/
If your hot water cylinder was installed before 1985 and it feels warm, you can buy an insulating cover to put over it to reduce heat loss.
The thermostat should be adjusted to 60 degrees C to keep water-heating costs down. It may be worthwhile arranging for all your hot water to be heated at night if this is not likely to cause too much inconvenience.
Savings can be made by washing clothes in cold water, having showers instead of baths, washing hands in cold water and turning off unnecessary lights. Leaving your electrical appliances on standby instead of turning them off can cost two or three dollars each week.
Hang out washing to dry and try to avoid using a dryer.
A heat pump or new refrigerator will be more energy efficient than your current appliance but they are expensive and can be noisy. The overall saving in electricity costs is often minimal.