No matter what kind of heater or furnace you have, you can help it work more efficiently. (If you have a hot water or steam heat system, be careful around the hot water and steam. If you have any questions, call a service technician.)
Check the air filters on furnaces and heat pumps once a month. Dust in them makes the blower work harder, leading to higher energy bills. So clean or replace the filters if you see dirt. Replacement filters are cheap, but if you don't have room to store them or never seem to have one on hand when you need one, consider getting a washable filter.
Vacuum out the warm-air registers and make sure they are not blocked by furniture, carpets or drapes. You can use little doo-hickeys that go over a register and redirect the air flow if moving the sofa or curtains is not an option.
If you have baseboards or radiators, clean them and, again, keep away furniture, carpets and drapes. You need air to flow to them from underneath to get the heat into your room. You also need air to flow over the tops of radiators, so stop storing the extra blankets there.
If you have radiators, you need to "bleed" them once or twice during the heating season. This medieval sounding practice is fairly simple. You use a radiator key to let the trapped air out of each radiator. Put a pan under the valve, which you'll find near the top of the radiator looking a little like the stem on a car tire. Hold the tap open with the key until all the air has escaped. You'll know you are done when only water comes out of the tap.
If you have a steam heat system, pull out your owners manual and start doing the maintenance recommended in it, like checking that the air vents are working, maintaining water levels, and removing sediments. Again, use caution. If you aren't sure what you are doing, ask a heating system technician to show you how to do these things safely.