A turbocharger is a device fitted in various machines (namely cars) with either forced-induction or internal combustion engines that takes the exhaust gasses from the engine and passes them through a turbine that spins at roughly 100,000 rpm and is used to drive an air compressor. The compressor compresses air to a pressure greater than that of the atmosphere so a larger mass of air passes into the engine - allowing for more fuel to be injected - causing a greater force to be produced in the combustion stroke of the engine's cycle (assuming a 4-stroke engine), so more power is produced.
The critical value with engines is termed the stoichiometric ratio (the correct chemical balance between any two substances - in this case air and fuel). Using cars as an example: In petrol engines the accelerator pedal controls a throttle (rotating valve - when the pedal's fully down the valve is fully open) in the air intake pipe; this is combined with a petrol injection system that injects the appropriate amount of petrol to achieve the stoichiometric ratio as combustion will only take place at roughly this ratio. Hence, more air being allowed into the engine (at a higher pressure) means more petrol can be injected so a more powerful combustion takes place in the cylinders increasing the power output. With diesel engines the air intake is constant (increased with the air pressure) while the accelerator pedal controls the diesel injection and is configured so that when fully depressed the stoichiometric ratio is attained. (Diesel engines do not require a stoichiometric ratio to achieve combustion, however, maximum efficiency is achieved when it's attained).
The alternative to turbocharging an engine is to supercharge it - a much older method that's been used since the 1880's! A supercharger is a form air pump / compressor that’s mechanically driven by the engine (i.e. either directly or indirectly joined to the crank shaft) and preforms the same function as the compressor does in a turbocharger.
Supercharging, despite increasing the performance at all engine speeds, runs the compressor directly off the engine and hence also decreases its brake thermal efficiency. Turbo charging, on the other hand, is used to boost the performance of the engine at higher speeds only (at lower speeds, the turbine doesn’t spin as fast so it has little effect on the power), and, because it uses exhaust gasses which would otherwise just be wasted, it has very little effect on the engine’s efficiency and produces more power than a supercharger when the engine’s running at the same speed.
I wouldn't say it's a complete guide, however, it's a start and should give you a good overview of what turbocharging (and supercharging) is all about. Hope it was of use - I'm sure there's plenty more lurking around the internet somewhere on it but feel free to ask if you need clarification on anything!