Check for spark. To do this, you can use a spark plug tester. You can alternatively take out the spark plug and lay the plug on the engine while still attached to the spark plug wire.
Turn over the engine and look for spark. If there is no spark, it is most likely the ignition coil that has gone bad. Replacing them is easy and they are cheap. The gap between the ignition coil and the flywheel must be .006 - .010".
The key thing to remember for any engine is that it needs fuel, air, compression, and spark. Those four things are what is essential for an engine to run correctly.
Check for compression. If you turn over the engine and feel some resistance, it has compression. If you have a compression tester, screw it into the spark plug hole and crank the engine over a few times. It should be between 90-110 psi. An engine that has low compression might have a blown head gasket. Don't worry, it's easy to do on these engines. Take off all of the head bolts (lay the bolts out in the order you took them out. Some bolts may be different sizes). Remove the cylinder head. It might be stuck on the engine so hit it with a rubber hammer to get it off. Look at the piston and the cylinder walls. Examine for scoring and pitting. There might be a lot of carbon buildup but that's ok. You can clean it off if you want with a wire brush. Before putting the cylinder head on, put blue Loctite on the threads of the bolts. This is important. Put the cylinder head back on with the new head gasket and thread the bolts in by hand. Don't use any tools first and make sure that the bolts are going on in the right order. Once the bolts are all the way on, it is time to torque the bolts to 140 in-lb. Torque them in the correct order.
Check the gaskets mating between the carburetor and the intake manifold and the engine. A leaking gasket can cause a vacuum leak which can make it run poorly or not at all. Gaskets are cheap to get and you can even make them yourself if you have the right tools.
