From what I understand, the turbo works off the exhaust. As the exhaust is heading for the turbo, it passes thru the intercooler to cool off the hot exhaust gases, making the air molecules closer together so that more air can be compressed into the cylinder by the turbo fan.
The turbo is driven by the exhuast gasses. You want to keep the heat (temp) up on the exhaust side because the heat of combustion makes the exhaust gasses expand. This expansion causes higher pressure (when driven thru a restriction-the turbo). The higher pressure blowing over the turbo blades (the 'hot' side) cause the blades to spin faster. This spins the shaft which has the compressor (or 'cold') side at the other end. The compressor side forces large amounts of air into the intake pipe. As you cram more air into the same size intake pipe the pressure goes up. This increases the amount of air that can be forced into the combustion chamber. Just add more fuel in proportion to the extra air and you get more heat in a higher volume of air so you can drive the piston down harder (MORE POWER). As for the intercooler, when you cram more air into the intake pipe by using a turbo the temp goes up just like when you run an air compressor in you garage. More air molecules shoved into a small space causes friction and heats up the air. The solution is to add an intercooler between the compressor and the engine to cool the incoming air so you can get more air molecules into the combustion chamber at a lower temperature. This cooler/denser air in the combustion chamber which will expand more during combustion--(again-MORE POWER). The intercooler helps to reduce the possibility of detonation too by having cooler air come into the cylinder which, when the fuel is mixed in, is far less likely to detonate because it is now cooler than the flash point of the air/fuel mixture. The water mist is used AFTER the compressor side of the turbo and BEFORE the engine (in the intake pipe) to cool the incoming air. It has a similar effect to the intercooler. As water evaporates it cools the air because it takes energy to make the water evaporate. It gets this energy (heat energy) from the hot compressed air in the intake pipe. This cools the air allowing more cool air into the combustion chamber. The water vapor in the combustion chamber also helps to prevent detonation. So, both intercoolers and water mist are very good things to have when you use a turbocharger. They will greatly increase the horse power and the life of the engine.
Just my $.04 worth. 8-} Stuart.