No Start Condition
When a chainsaw wont start but the engine turns over freely its a no start condition. This is the most common chainsaw issue and there are many possible reasons for it. A few tips to fix this kind of condition are replace your spark plug as its the most likely part to not be functioning properly and make sure your wiring, ignition coils and switches are all working properly.
Start Stop Condition
This is the name for chainsaws that stop under load or run for a few seconds then die. Lots of parts can cause this issue but the most likely reason would be a plugged spark arrestor screen that would prevent exhaust from properly leaving the engine. You should also check if there are any clogged ports in the carburetor that would affect its ability to inject the right amount of fuel or air into the engine. Other possible but less likely causes are faulty spark plugs, bad gas caps or bad fuel filters.
A hard to start chainsaw engine can be caused by hugely varied list of parts. Nearly any component of a fuel, spark or air system can cause this problem. The first thing to check is that you are getting a good spark from your spark plug. If that doesn't work try cleaning the intake and exhaust. Next you should check any fuel delivery problems to make sure its getting enough.
Bad Engine Performance
Just because it starts and runs doesn't mean it's not suffering from performance issues. It could sputter or lack power and this normally means that your engine is out of tune. The easiest way to fix this is to keep replacing temp parts such as air filters when they are used up.