fan draws air from house into system
gas burners create heat in heat exchanger
hot air is distributed through vents
cooling coils inside plenum cool the air
Understand the System
To explain the components of a forced air system: a fan draws air from the house into the system through return air vents (Image 1). During cold weather, gas burners create heat in the heat exchanger (Image 2), which in turn heats the air. The hot air goes up into the plenum and from there flows to the supply trunk line (Image 3) where it is distributed through vents throughout the rest of the home.
The conditioned air then re-circulates back into the system as needed. During hot weather, you turn on the air conditioner and cooling coils inside the plenum (Image 4) then cool the air, which is then distributed throughout the house.
You need a load calculation to make sure the furnace is large enough to supply the new room. You can get it online from companies like DuctWork or go to local HVAC pros to get a load calculation worked out. Generally speaking, if the room existed when the house was completed, the furnace is probably powerful enough. If it is an addition that was added after the house was built, you may need a new furnace.
A couple other components to a gas forced air system is a source of fresh air from outside the house to aid in combustion, and you'll notice chimney pipes that carry flue gases from the hot water heater and the furnace to the outside of the house.