When troubleshooting a small engine that isn't starting, one of the first things you'll want to do is check for spark. This can be done with a simple test light.
To check for spark, first make sure that the spark plug is properly seated in the engine. Then remove the kill switch wire from the spark plug. Next, touch the end of the test light to the tip of the spark plug while someone cranks over the engine. If there's spark, you'll see the test light illuminate.
If there's no spark, then you'll need to further diagnose the problem. It could be an issue with the ignition system or there could be a fuel delivery problem. But if you're able to rule out those other potential issues, then it's likely that there's a problem with either the stator or flywheel key on your small engine.