If you ignore the fuel supply and ignition systems, an engine is basically an air pump. The pump pulls air through the intake and pushes air out the exhaust. The dry compression test tells you how well the pump is working. As the engine warms up, the pistons expand and the ring seal gets tighter, and that's why you warm the engine first. If one or more cylinders fail the dry compression test, then you have a leak in your pump. Possible leaks include worn rings/cylinder walls, leaking intake valves, leaking exhaust valves, blown head gasket or cracks in the head or block (less common). The wet compression test (oil added into the cylinder) helps the rings seal better and if the compression gets better, then ring blowby is the suspected. If the wet test does not improve compression, then valves or head gasket are suspect. Normally, a blown head gasket will yield other symptoms (bubbles in radiator, white smoke in exhaust, overheating, etc.). The condition of the spark plugs is another good diagnostic - a black, oily plug on the cylinder with low compression indicates worn rings or worn valve guides. The leak down test is useful because you can listen for the leak (leaking intake valves blow into the intake, leaking exhaust valves blow into the exhaust system, worn rings blow into the crank case). The most common valve leak is on the exhaust side because of heat. An exhaust valve that does not close all the way will burn and leak. Another old school diagnostic tool is the vacuum gauge. Valve problems cause the engine's vacuum reading to bounce up and down. There is no one single test that gives you an answer, you must gather all the info you can and then play detective.
If you determine that the rings are not sealing to the cylinder walls, then a tear down is in order. The cylinder bores wear more at the top than the bottom, and the amount of bore taper and overall cylinder wear determine whether you can get by with honing/new rings or a full rebuild (bore the cylinders oversize and get new pistons and rings).
