Cold air intakes
Cold air induction can add (or maintain) power by feeding the engine colder outside air rather than the engine ingesting the preheated underhood air. The difference can be fairly significant, especially with high output/high performance engines.
Cold air induction can allow for richer carburetion tuning with an increase in power. It can also reduce the tendency for detonation.
 Ford Thunderbolt
When the subject of cold air induction comes up, the first car some may think of is the 1964 Ford Fairlane Thunderbolt.
Dearborn Steel Tubing (known as DST) purpose built these cars for NHRA Super Stock drag racing for Ford. The engines that they used were the (very underrated) 425 HP, 427 cid high riser side oiler.
To feed cold air to a engine of this size required large (~6" diameter) tubing connected to a large aluminum air plenum box atop the dual 4 barrel carbs. The large air box required a bulge in the hood, and to get cold air from the frontal area to the large intake box, the designers used the area where the inner headlights normally resided for the intake. They added grills to keep out large debris, and ran the ducting up to the intake box (seen below). The result was the iconic look of the Ford Thunderbolt.
 Fabricating a cold air induction system
This is really quite simple; a great project for the budding automotive enthusiast. A homemade cold air intake can be built using nothing more complicated than coffee cans and dryer duct, the can can be pop riveted to the air cleaner sides after cutting a hole the shape and size desired. Then route the dryer ducting to a source of outside air. On older vehicles, this was usually from the grill area or under the bumper. This isn't the prettiest or most efficient set-up, but illustrates the basic concept can be adapted using low-tech methods and materials.
 Design considerations
Generally speaking, bigger is better because it is less restrictive. However, packaging the system under the hood has to be a consideration.
First you need to know the diameter of the stock intake tubing (if it is to be used/reused) or the size and shape of the air cleaner snorkel if it's to be used. If using a remote filter like a cone type reusable gauze filter, the location needs to be selected based on available space and a suitable carb "hat" needs to be bought or fabricated.
 Late model production vehicles
In most cases, the late model passenger car/light trucks on the road today are using some sort of cold air intake. If the air filter housing/box is located on one side or the other of the engine compartment, and has ducting that goes through the inner fender, this duct work is pulling in outside air. Most aftermarket cold air intake kits include ducting that is smooth, not ribbed or corrugated. This allows for less disruption of the airflow, which is also beneficial in combination with the cold air intake.
A high flow air filter in a stock intake box/housing with smooth ducts can work well on late model applications, sometimes as well as the high dollar kits sold in the aftermarket. In these cases the only "advantage" to the aftermarket kit is the looks.
 Potential gains
A law of physics states that for each 10º drop in air temperature going into the motor, power will pick up by 1%. This is because when the air is colder, it is more dense and therefore contains more oxygen. So potentially, a 100º drop in air temperature would equate to a 10% increase in power. On a 400 hp motor, this would equal a 40 hp power increase.
Of course, a tuner would have to compensate for more oxygen by jetting richer to correct the air/fuel mixture. The later model EFI systems sense more oxygen and automatically richen the mixture.