At the top of the piston stroke, the diesel fuel is injected into the combustion chamber at high pressure, then through an atomizing nozzle, it mixes with the hot high pressured air. The resulting mixture will ignite and burn very rapidly. This combustion will cause the gas in the chamber to heat up rapidly, which increases the pressure and forces the piston downwards.
The connecting rod will transmit this motion to the crankshaft. The scavenging of the engine is either done by ports or valves. To get the most out of a diesel engine, use of a turbocharger to compress the intake of air is vital. You can also use an aftercooler or intercooler to cool the intake air after compression by the turbocharger to further increase your efficiency.
An important part of older diesel engines was the govenor, which limited the speed of the engine by controlling the rate of fuel that was delivered. Unlike gas engines, the air that comes in is not throttled, so the engine would overspeed if this wasn't done. Older style injection systems were driven by a gear system that came from the engine.
The diesel engine is truly an advancement to vehicles as we know it. As technology gets better, you can expect the diesel engine to get better as well, possibly even proving just how much better it is to the gasoline engine.