A furnace draws air from the house into a ductwork system, taking it to an area where it is warmed before being delivered back to living spaces. Newer furnaces use blowers to recirculate the warmed air. A furnace may be fueled with gas, electricity, oil, or even coal or wood.

Circulating air is drawn through a filter that helps rid the house of dust and other particles.
Gas and oil furnaces have a pilot light that warms a heat exchange unit, which in turn warms the air before it is circulated back through the house. These furnaces have a flue where exhaust gases vent to the outside.
An electric furnace uses heating strips, or elements, to warm the air.
A wood or coal furnace has a sealed firebox where the fuel is burned, and a heat exchanger where air is warmed before delivery.
Metal vents that allow warmed air to escape from the system and into the house are usually found in the floors or on walls in living areas.
The home's temperature is controlled by changing the settings on a thermostat, usually positioned on a wall at eye-level. The thermostat shows the current temperature of the room.
Tanks for oil furnaces are sometimes buried. If they leak, they become an environmental hazard.
Electric Heat Pump
Heat pumps work by shuffling heat from one place to another. They also serve as air conditioners during warm weather.

Heat pumps extract warmth from outdoor air, from ground or surface water, or from the earth. The air is warmed more by the system if necessary, then circulated through the house.
You'll find metal vents and filters similar to those used for forced air furnaces. The thermostat may appear similar, but will also include controls for air conditioning.
The outdoor unit usually states 'heat pump' on its label.
Radiant Baseboard Heat

Baseboard heaters are often visible as long, metal units with electrical elements inside. Each unit has its own control, which may be marked in increments from low-to-high, but will not show the room's current temperature.

You might see baseboard heaters used as a home's sole source of heat, or for supplemental heat in cooler rooms or rooms that were difficult to outfit with ductwork. They are typically more expensive to operate than furnaces.

Radiant Ceiling or Floor Heat

Radiant systems warm objects in much the same way as the sun does. No blowers are used.

Electric radiant elements are installed in floors or ceilings. In the examples I've seen, each area has a dial control similar to the ones that operate baseboard heating units. Heating elements can also be installed in walls, but that location is less common.

Hydronic Heating is another type of radiant heat, where hot water flows through tubes under the floor or through units that resemble baseboard heaters.

A hydronic system might be installed in ceilings.
Hydronic heating systems are sometimes used under concrete in driveways to keep snow and ice from accumulating.
Hydronic heating systems include a boiler that warms the circulating water.

Space Heaters

You might see portable space heaters that are electric or fueled by gas or kerosene. These should not be used to qualify an area as heated living space.
Gas space heaters are common in some areas. They may be freestanding or may be attached to a wall. If permanently attached, they do allow an area to be counted as heated living space (provided other qualifications are met).