Society has been heating with fire since the caveman days. In 2010, fire is precisely controlled in furnaces and modern fireplaces. The fire heats the air, and hot air is circulated through ducts by an electrically operated blower. The fuel for the fire can be natural or propane gas, fuel oil or bio-fuel oil made out of vegetable oil. Fireplaces, some furnaces and fire stoves use wood or wood pellets as fuel. All fire sources produce smoke and fumes, and these must be vented to the outdoors via a flue and chimney.
Solar heating is a viable option for the daylight hours. Solar panels are installed on the roof, and heat the internal air inside the panel or fluid. The heated air is blown into the living area, heating it. Systems range from very simple panels, with an electric fan blower, to very high-tech computer-controlled systems. As a backup for the night hours, you should have an alternative method of heating, such as a furnace or fire stoves.
Electrical heating is a very clean method, but it is energy intensive. A simple room heater may draw 1,000 watts of power. On the plus side, electricity can be obtained from a variety of sources. Some of these would include the public utility grid, photovoltaic panels or "solar" panels, wind turbines, or hydroelectric power if you live by a river. The initial costs may be high, since you are, in essence, building your own power generating plant. For example, the Connecticut Clean Energy Fund states that a 2 kilowatt photovoltaic system may cost $16,000 to as much as $20,000 in 2010.
Heat pumps use electricity to drive them, but the heat itself is "drawn" from the air or ground. Heat pumps are more than just heating units. In the summertime, their operation is reversed, so they become air-conditioners. While they are energy efficient, ground-source heat pumps are expensive to install. The Ohio State University reported that a nominal ground source heat pump system for a home costs a minimum of $8,000 to install in 2010.