I am not aware of a troubleshooting guide but I think I can provide some help. I find that the easiest way to troubleshoot gas engines is to think of the engine in terms of systems. On a small trimmer engine you really only need to be concerned with 3 systems. Fuel, ignition and compression. There are a few simple tests that you can do to eliminate each system and find the problem area.
I always start with the fuel system as it seems like the vast majority of won't start issues are related to the carburetor. This is a simple system to test. Remove the air filter and spray a bit of starting fluid into the carburetor then try starting the engine. If it fires for a second you know that you have a fuel delivery system. Most problems here will be due to dirt or debris in the carb. On an older machine the diaphragm and reed valves in the carb might have dried out. Cleaning or rebuilding the carb should solve the problem. Other fuel system issues can be related to crack fuel lines or a plugged fuel filter.
If the fuel system checks out OK then take a look at the ignition system next. The most common failure in the ignition system is the spark plug. The easiest way to test for a bad plug is to simply replace it. If the plug is OK then you will need to test the ignition coil. You will need a spark tester to do this. The spark tester attaches to the plug wire on one side and to the plug or engine block on the other. You do need a spark tester to accurately test for spark. Simply removing the plug, grounding it to the block and then looking for a spark visually just doesn't cut it. Bad ignition coils are very rare now days but they do occasionally fail.
The last system to test is the compression system. A 2-cycle engine should typically have compression somewhere between 70 to 120 psi with 90 to 100 psi being normal. You will need a compression tester to check the cylinder compression. Low compression in a 2-cycle engine is usually due to worn piston rings and the cylinder. This is typically an expensive and difficult repair. Often low compression is a death sentence for most tools.
I hope this helps you diagnose your small engines.