Firstly Black smoke. This has often been called "unburn't" fuel. Mmmm, kinda true but technically incorrect. Black smoke is fuel that has been burn't with not enough oxygen present. Firstly, we need to think about Chemistry here. The fuel particles, or little droplets of Hydrocarbons, are chemicaly reacting and resulting in rapid oxidation, producing tremendous heat and expansion of gases in the way that we can harness this power and use it to move the Piston in the cylinder. In a proper and correct burn, the immense pressure, heat and oxygen will cause all the particles to oxidize and most all the carbon is burnt away. Not enough oxygen results in the particles not burning efficiently and completely, leaving carbon particles. The carbon is black of course and we see it being blown out the back of the exhaust as black smoke.

White smoke is pure fuel and is more technically correct to say it is "unburnt" fuel. The Diesel engine works by producing an enormous amount of pressure in the cylinder. The Piston is forced up and compresses the Air in the cylinder. The pressure is so immense, that the Air reaches a very very high temperature and just as the Piston gets to the top of the cylinder, the fuel is sprayed into the cylinder under immense pressure through a very small hole. This produces a very fine mist of Diesel fuel that rapidly heats and explodes into flame. But if the pressure of the cylinder is down, maybe due to valve leaks or cylinder wear, the temperature is still hot enough to vaporize the Mist of Diesel, but not quite hot enough to cause it to combust. So we see a "white smoke" of Diesel vapor being ejected out the exhaust.

Blue smoke is engine lubrication oil being burned in the cylinder along with the fuel. I am not sure why the blue exactly, it maybe due to additives put into lubrication oil to do the job and Lubrication Oil has a much higher ignition point than fuel oil, so tends not to burn very well at all.

Water vapour in exhaust is much harder to diagnose. Especially in water cooled exhaust system. Usually water in the exhaust will mean it is getting into the cylinders and the smallest drop of water robs the cylinder of much needed heat to start the combustion. So chances are, a water problem will be seen as an engine being difficult to start, an engine that runs ruffly on a couple of cylinders or an engine not wanting to start at all. Because the gap in the cylinder is so small when the piston is hard up, very little water in the cylinder can result in the piston locking of hydraulicing at the top of it's compression stroke. I have seen this happen and the result can be from no damage to the worst I have seen, the block being cracked and the conrod being bent.

PLEASE NOTE: Any of these smoke signs coming from an exhaust may not always mean that you have X problem. There are many other tests that need to be done to determine just what exactly the problem maybe. But smoke does show that some problem, maybe minor, maybe seriously, is most likely present.