If you are having trouble starting your twostroker then here are a few tips and tricks for you to get your engine started again.
First and foremost – two stroke engines are very easy to start (yes even when they are cold) so if the engine does not start after a few kicks or pulls on the starter then you should consider looking for symptoms. The easiest checks you can make are related to combustion. For the combustion to happen you need air, burning material (petrol) and igniter (spark plug).
Of course there is some common sense required, so that if the engine makes a squeaking or rattling noise, or there is no petrol in the tank then approach likewise and use your common sense. But below I will briefly describe how I would approach the troubleshooting.
Spark: we will start off with the spark plug inspection as it tells a lot about the health of the engine and might easily give an indication about what might be an issue. After pulling the spark plug and the tip of the plug is wet it clearly states that there is fuel flow into the engine. But what our aim now should be is to check if the spark is actually generated. For that you need to put back the spark plug wire on the plug, ground the spark plug and kickstart the engine. For grounding it is good to connect the spark plugs threaded/metal part to the engine case while keeping the plug wire still on. While you kickstart the engine now or roll the starter you should see the actual spark on the tip of the plug. If it is not there then there is obviously an issue with the plug or electrical side of the engine. Before doing anything else change the spark plug (even if it is new) and see if you get other results.
There is tons of information on google on how to read spark plugs. But moving on to the next required topic
Fuel: The basics of course are to make sure that you have gas in the tank, it is flowing into the carb (fuel valve open, not blocked). If the bike has been on the stand for quite some time, for example over the winter, then it might as well be that the fuel is stale or there is some water through condensation. As the water is more tense than petrol then it is sitting in the bottom of the tank. In both cases you need to drain the tank as well the carburetor float boal. If there happens to be any debris in the tank or carb passages then petrol, carb cleaner and pressured air can be used to help you out.
Air: It is unlikely that the air flow is an issue on a two stroke engine but just make sure that the airfilter is clean and there are no obstacles. It may happen that there is some debris from the air passages into the carb but in that case carb cleaning should do it.
The above is very simplistic approach but hopefully this helps a to get things going. If not then diving deeper is required.