Thats pretty much it, a turbo uses exhaust gasses to spin a turbine, which is connected to a centrifugal compressor via a shaft, the compressor sucks air in from your intake, compresses it and squeezes it into your inlet manifold then into your cylinders. But as hot gasses dont combust as well as cool gasses the compressed gas is sent through a heat exchanger (your intercooler) then into your cylinders.
Its then mixed with fuel, compressed further by your pistons, and goes bang, it then goes out the cylinder via the exhaust manifold, down through the turbo turbine, which it spins up, making the compressor spin and the whole process starts again!!!