Turbocompressor removes energy from the exhaust gases. The gas exiting the engine is hot and has high velocity. It expands trough the turbine and generates power that is used to run the compressor. The temperature and especially the velocity of the exhaust gases downstream of the turbine are significantly lower. The energy from the exhaust gases is then transferred to intake air that is forced in to engine instead using the engine piston to suck it in. That is your gain. Intercooler increases the efficiency of the whole process. The compressed air is hot therefore has larger volume than cooler gas of the same pressure. Removing some of the heat decreases its volume. Therefore the velocity of the air in the suction decreases. Since the resistance of the suction (sum of all resistances such as filter, suction duct, manifold, suction valve etc.) changes with square of velocity the intercooling heat loss is made up by gains achieved by lower air velocity. The end result is that you can stuff more air (oxygen molecules) in the combustion chamber, burn more fuel and get more power. This works up to the point of mechanical and material limits of the engine. Increasing power beyond such limit will destroy the engine. In example some racing engines last only several hours.
When I was a teenager I used to race quite successfully small boats (you know the big heart and little brain syndrome). Typical boat engine produced about 50 HP from 175 CC displacement burning pure methylalcohol. That is about 285 HP/liter. The trade off was that the engine lasted about 8 hours between overhauls.
Typical tractor diesel produces about 20 HP/liter. That is why they last forever.
For SFC and other interesting data google "Specific fuel consumption, piston engine".