You can only get so much air into an engine if you rely on a combination of atmospheric pressure and engine vacuum. If you force air in with a turbo or supercharger, you will get a much bigger gulp of air and fuel. The more you get in, the faster you go! There are many ways of doing this.
Turbocharging
What comes out of your exhaust pipe is waste product. In a normally aspirated non-turbo engine the gas fires down the exhaust pipe containing lots of momentum and then escapes into the atmosphere, doing its bit for pollution on the way. If you pass this fast moving gas through a cast iron passage containing a turbine wheel, it makes it spin. If you connect that via a common shaft to another wheel with propellers closely fitted in an aluminium housing, it would suck air in, throw it against the walls due to centrifugal force, squash it and then force it out the other side. Now the air is pressurised and travelling much faster. In effect you have created an air pump which is called a compressor. Connect this to a tube feeding your engines induction system and you have instantly got a supply of as much compressed air as your engine can handle. The more quickly you spin the turbines, the more air you get in and the faster your car will go.
This is the principle of the turbo charger, the compressed air and product called the boost. This gives you lots of horsepower and torque. It isn't as simple as it sounds because you need a method of regulation. If you carried on spinning the turbine, you would create endless boost pressure, eventually blowing everything up! As a result, when the compressor reaches the required level, an actuator on the side of the turbo pushes a door open in the turbine housing called the wastegate. The exhaust gas is then rerouted down the exhaust pipe, the turbo stops spinning and the boost stops.
Bigger/Hybrid Turbos
Probably the most common Turbo is Garrett Air Research, made in sizes according to boost range (T2.5, R5 GT Turbo, T3, RS Turbo, T3.5, T4, RS500). Fit a bigger turbo and you get more boost. But there are ways to get more out of your existing turbo. If you increase the size of the turbine and/or its passages it will spin faster. You can impede flow too, controlled by trimming back the blades. If you fit bigger, more propeller blades in the compressor it will displace more.
The size of the turbo fitted is critical to the engines state of tune. Sometimes you need an in between point from one size of turbo to another. What you need is a hybrid. This is a turbo that has been modified to produce more boost. In addition its insides have been uprated to cope with the faster spinning.
Turbo Engine
Turbo-charged engines need a lower compression ratio than a normally aspirated one. This means that you can't just fix a turbo onto a standard engine and expect it to work.
Because the air is compressed, you get more in, so extra air means extra fuel, which in turn creates a larger volume and this means you need a larger combustion chamber for it all to fit into. Enlarging the combustion chamber in the head, or piston, lowers the compression.
Intercooler
Compressed air produces heat, meaning it expands so that its volume is greater. Performance means getting as great a volume of air/fuel into the combustion chamber as possible. But warm air is greater in volume and wastes space.
An intercooler works in the same way as a radiator, it goes in hot, through a series of tubes with cold air taking the heat away and comes out cold. Instead of feeding in water like a radiator, you feed in hot compressed air and feeding out cold air. You cannot over intercool so the bigger the better.
Nitrous Oxide Injection
Although not strictly forced induction, Nitrous Oxide Injection, or liquid supercharging, has the same effect. Its a way of instantly raising the level of oxygen supplied to the intake charge, which means more power. Squirt Nitrous into the airflow and the heat of the combustion breaks it up into components of nitrogen and oxygen. Nitrogen acts as a carrier and is inert but it becomes very cold when it turns into a gas. It therefore lowers the charge temperature and as with intercooling, becomes denser. The air you and your engine breathe is 78% nitrogen, 21% oxygen and 1% other gases. Nitrous Oxide contains 36% oxygen, so is better than air. By squirting this into the charge, you instantly raise the level of oxygen which is part of the charge added to the fuel to make it combust. But if you added just Nitrous, you would get a mixture rich in oxygen, lean on fuel. So this means you add more fuel which means more power.
Solenoids & Injectors
A nitrous system consists of the bottle of gas under very high pressure, feeding lines into solenoids (electric gates). These release an amount of gas into the injectors when you hit the nitrous switch. In most systems, there are two sets of solenoids, one for gas and one for fuel. You must get the ratio right or BOOM.
Dump Valves
The principle of a dump valve is that it keeps the flow of charge moving. In very high boost situations such as racing, so much boost is made that when you come off throttle, to change gear for example it has nowhere to go. You can't stop the flow of air so it hits the throttle plate and turns back on itself shooting back the compressor wheel.
This reverse charge could stall the compressor, slowing down the car. If you vent off or dump the unwanted charge, you keep the momentum of the compressor wheel up.
Supercharging
A supercharger (or blower) is almost identical to a turbo except that its pulley driven from the crank rather than the exhaust gas spinning the turbine.
There are plenty of types of supercharger, the traditional type sits on top of the engine between the induction system and the combustion chamber. Turbos normally blow into the induction system, a traditional supercharger sucks.
There are two main types of supercharger, the traditional Rootes and the centrifugal which works in a similar way to a turbos compression.
The main advantage a supercharger has over a turbo is that the effect is instant. The boost starts as soon as the crank is turning and, as such, the throttle response is linear. Even on idle the supercharger is producing boost so there is no lag. Since it almost doubles the horsepower, a supercharged engine behaves just like one of a larger capacity.
The downside to a supercharger is that it takes horsepower to spin it. This isn't a worry for the centrifugal type because they are freer running than the Rootes blowers. Like turbos, superchargers are rated according to the boost they produce.