Right, so no forced induction bypasses the combustion process, they increase the power (i.e., torque) that's generated, by forcing more air into the engine during that same process.
If you'll indulge me expanding on this a bit:
(Warning, another infamous wall of text ahead)
One major engine parameter is displacement. It's important to remember effectively an engine is an air pump, and the displacement dictates just how much air the engine is capable of pumping in and out in total in a complete combustion cycle(which means two complete rotations for virtually any gasoline automobile engine you're likely to encounter, and increasingly even in small engines).
In a "perfect" engine, we mix that air with gasoline in the exact correct amount that is needed for complete combustion of the gasoline(and no more), then light that mixture at exactly the correct time. In the cylinder where this has occurred, of course as this air/fuel mixture burns, the amount of gas increases in the cylinder dramatically, and we use this increased gas production ideally to push a piston. The crankshaft converts that linear motion into rotational motion.
The "perfect"(stoichiometric) ratio of air to gasoline is often given as 14.7:1, although with modern alcohol heavy fuels it may be closer to 12.5:1 or so. In any case, we need a metering device to meter the exact amount of(vapor phase) gasoline according to the air being pumped in by the engine. For a really long time, the most common way of doing this was with a relatively crude mechanical device called a carburetor. Carburetor rely on the principle that when air is put through a constricted area(called a choke or a venturi in carburetor speak), the velocity increases and the pressure decreases(the same principle that makes airplanes fly). This creates a low pressure region inside the restriction, which allows aeresolized gasoline to be "sucked" into the air stream. There are various strategies to ensure correct metering under different conditions, but none are perfect and carburetors will be "off" a bit under most conditions.
The way it's almost universally done now on vehicles is using a system called fuel injection. Essentially, in electronic fuel injection, a sensor measures the amount of air flowing into the engine(there are a couple of different strategies to measure this either directly or indirectly), the computer calculates how much gasoline is needed, and a tiny pump provides a metered "squirt" of gasoline that mixes with the air and then is sucked into the cylinder. As a check for all of this, an oxygen sensor in the exhaust pipe then measures whether or not the correct amount of fuel was metered, and it's adjusted. This provides nearly perfect fuel metering under all conditions, and actually provides a bunch of benefits to both engine life and fuel economy. Fuel injection can also adjust for the current driving conditions(acceleration usually wants a bit more gasoline, cruising a bit more air).
That's all a bit of a diversion, though, to say that ultimately the amount of air, and consequently the amount of fuel, we can put into the engine is governed entirely by how much air the engine can suck in. This sort of set up is called a "naturally aspirated" engine. There are restrictions that keep the engine from sucking in all the air its capable of. The single major one is user controlled-the throttle(which is a valve that opens and closes as needed). There are other things in the design that can also restrict this. When, how much, and for how long the intake valves are open are another major one. This is governed by something called the cam. Traditionally, cams are designed for a specific application, as doing things like increasing the lift(how far the valves open) and duration(how long they're open) tend to help at the top end but can cause rough running and loss of power at lower engine speeds. Often an engine with too aggressive of a cam will have a very rough idle, and also be difficult to even get moving. BTW, virtually all engines these days, including pushrod overhead valve engines, use some form of variable cam technology. Basically, using a variety of methods, the can vary the cam timing and/or profile based on engine RPM and load, which lets you have a cam set-up better suited to a range of conditions.
Putting all of that aside, though, if we want to get more air(and consequently more fuel) into an engine, we basically have two ways of doing it. The first and on paper simplest is to just increase the displacement of the engine. There are three factors that determine displacement-the bore size of each cylinder, the stroke length(how far the piston moves up and down in the bore) and finally the number of cylinders. Of course if we're using a single engine block casting, there's a limit to how much we increase each parameter. With bore size, we can simply run out of room to not have bores overlap(or not leave enough space for strength or cooling between them). Stroke can be increased up to a point-it's sometimes done in the aftermarket by grinding rod journals smaller and "offset" from their old position, then using a rod with a smaller big end, but this depends on such a rod being available. The manufacturers can design a crankshaft with the rod journals offset more, but again you can run out of room to do this. In the heyday of American V8s, most makes made both a "big block" and a "small block" V8. The small block often topped out somewhere between 5.5 and 6L(prime example-the small block Chevy 350 at 5.7L) where a big block could go up to 8L or so. Modern small block engines like the Chevy LS series and the new Chrysler HEMI can venture up into the mid 6L range(Ford does have a new "big block" 7.3L that looks to be a great engine for the right applications).
In any case, the market is largely moving toward smaller physical sizes of power plants. Regardless of that, though, large displacement naturally aspirated engines do have their downsides. One of them is that even under light load, they still use a lot of gasoline.
We do have ways of getting additional oxygen into the cylinder, but that's side tracking a bit. Alcohol based fuels require less additional oxygen to burn stoichiometrically. Compounds like nitrous oxide can be put into the air coming into the engine, which break down during combustion to add oxygen. You'll hear of some of these in racing, including cars that add nitrous oxide(usually "nitrous"), or often drag cars run on nearly pure methanol. These days, fuel that contains 85% ethanol is fairly easy to find(the gas station up the street from me has it) and even ordinary street cars can be designed to use it along with standard gasoline. E85, as its called, usually gives a nice performance boost to cars(although cost is often the main reason to use it).
All of the above assumes that we're using air at atmospheric pressure. Air that is raised above atmospheric pressure is more dense, and consequently a greater number of air molecules can fit in a cylinder of a given size than if simply using atmospheric pressure air. To go above atmospheric pressure, we can use a pump in the intake path. These pumps can give a significant performance improvement. More so, we can adjust the exact pressure increase they're providing, to allow more power on tap when needed but shut it off when not. This can let us have our cake and eat it too, so to speak.
These pumps to increase pressures can be directly driven off the engine. When that's done, it's called a supercharger. We can also use exhaust gas to turn the pump, and this is called a turbocharger. Both have been around for a while, and some engines(for various reasons) respond better to one than the other.
BTW, I do take issue with the common statement of turbochargers using "free" power rather than robbing it off the engine. The other half of the whole "air pump" idea of an engine is that after the fuel/air in the cylinder has burned, the exhaust products have to get out of the cylinder. They are at much higher pressure than ambient, so they will tend to flow out on their own once the exhaust valve is open. Still, though, the cylinder's upward motion has to be used to push the last of the exhaust gases out. A turbocharger is a BIG obstruction in the exhaust path that has to be overcome, and the engine does expend energy on the exhaust stroke to overcome the turbo. Like with a supercharger, the trade-off is worth it since the energy used is less than what can be gained, but it's still there.
