Make sure you are using a high octane gasoline mixed with a high quality 2-stroke oil. 91 octane or higher is recommended. The gas-oil ratio is 25:1 which is 5 ounces of oil per gallon. Using octane booster is not recommended. Do not use oil labeled TCW3, marine or outboard oil as your engine will not perform well with this oil. An ethanol remover is recommended.
Check to make sure your spark plug is clean and working. Remove the plug from the engine and inspect the tip. If it is clogged up it will need to be cleaned or replaced. After the plug is removed, check if the plug is working by: attaching the wire to the top of the plug, and place the tip of the plug very close to the metal of the cylinder. Pull the pull start a few times. A spark should jump from the plug to the cylinder. If no spark or weak spark, replace the plug, ensure the ignition coil and flywheel are properly gapped, then check again. If still no spark – you likely have a problem with the ignition coil, and will need to replace it.
Check to make sure your carburetor is properly tuned. Rotate the ‘H’ and ‘L’ screws on the side of the carb fully clockwise (‘closed’). Then, turn the L screw counterclockwise (‘open’) 1 and 1/4 turns. Turn the H screw open 1 and 1/2 turns. You may need to adjust these screws slightly in either direction to find correct tuning for your carb.
Your engine may be flooded. If you have pushed the primer bulb many times, or pulled the pull start a lot of times, the engine may be flooded. Remove the spark plug, and allow all the fuel in the cylinder to evaporate. You can speed up this process by blowing on it with a hair dryer, and/or by turning the engine upside down with the spark plug out and pulling the starter a few times to purge accumulated fuel from the crankcase.
Your compression may be bad. If you have an older engine, the piston ring may need replacement.
Check your carb gasket, intake gasket, cylinder gasket, and crankcase gasket. Can you hear air whooshing out of the cylinder gasket or crankcase gasket when you pull the starter? Is air leaking in the manifold gasket behind the carb? A gasket leak results in a loss of compression and/or improperly mixed fuel and air. An easy way to check for intake leaks is to spray the intake manifold and area surrounding it with WD-40. If the idle changes after you spray the WD-40, there is an intake air leak. Common areas for leaks are between the manifold and the cylinder, and between the carb and the intake manifold. Inspect the manifold, carb gasket, and intake gasket for cracks or other signs of damage, and replace if necessary.
If your engine still won’t start, you will likely need professional service on your engine.