We have been lucky enough to not have a very cold winter but it is never a bad time to save some energy. Hot water is an area you can save some easy money.
Heating water accounts for 14%-25% of the energy used in a home. The average gas fired tank water heaters found in most homes are about 55-70% efficient and electric ones are around 90%. While being more efficient electricity is more expensive than the fuel.
There are some easy ways to save that the average person can tackle. One well known thing to do is insulate the tank. There is varied opinions on it's effectiveness but some state it can save 4%-9% on heating cost by reducing standby loss. You should first check if your warranty would be void by adding a blanket. You get the best return if your water heater is located in the garage or some other cold area. Electric water heaters can have a foam pad placed on top since there is no flue.
Still along the lines of insulation is hot water pipes. If your hot water pipes are located in a cold crawlspace they should be insulated. Uninsulated pipes in crawlspaces can loose 2-4 degrees of heat. Pipe insulation should be sized for the pipe and it's recommended to keep the joint on the bottom and tape all seams. Spray foam can be used where pipes enter into the living area to keep the cold air from inside the walls.
A very simple way to save is keep your hot water temperature set at 120 degrees. For every 10 degrees your hot water heater is turned up it cost an additional 3%-5%. It not only cost more but the hotter the water is the more dangerous it is. Scalding at 120° can happen in 5 minutes, 130° in 30 seconds, 140° in 6 seconds, 150° in 2 seconds. For a gas water heater it's as easy as turning the dial. On an electric model it requires opening the element cover. A plumber or often the Electric Utility can do this for you.
Another simple thing you can do is drain your water heater. Depending on the sediment in your water you should drain about a gallon out every month to every 6 months. Sediment can reduce it's efficiency by 10% on fuel fired units and can damage heating elements on electric ones. The drain on some are all plastic and can be easily damaged or broken off, as a Home Inspector I often find these leaking. You might need to have a plumber come drain it. While they are there have them replace the drain valve with a new one made of brass that will allow you to drain it often with no problems. Some places will offer draining service for free as a marketing tool to get business. Some newer tanks are made to keep sediment off the bottom and don't need regular draining. If you hear popping or crackling when the water heater is running it could be sediment on the bottom.
Turn the water off. Monitoring your hot water use is one of the best ways to save. Hot water that goes down the drain was paid to be heated.
If going to be away more than three days turn the water heater to "Vacation" and on electric models you can turn off the breaker.