This is almost always a fuel delivery or starting procedure issue. Let's walk through the cold start steps.
First, make sure the chain brake is engaged. This locks the chain and is a safety requirement for starting. Locate the master control lever on the engine. Move it to the choke position (the snowflake symbol). If your model has a manual fuel pump, press the primer bulb at least five times, even if it looks full. This ensures fuel is in the carburetor.
Now, place the saw on a firm, flat surface. Hold the front handle down with your left hand. With your right foot in the rear handle, pull the starter rope briskly until the engine attempts to fire (you'll hear a cough). At that point, immediately move the master control lever from the choke position to the half-throttle or fast idle position (the rabbit symbol). Pull the starter rope again. It should start. If it doesn't, go back to the choke position and repeat the priming and pulling process.
If that didn't work: Check your fuel. It must be a fresh mix of gasoline and the correct 2-stroke engine oil. Old gas won't ignite properly. Also, check the spark plug. The electrode gap needs to be 0.5 mm. A fouled or damaged plug won't spark.
Heads up: Once the engine is running, let it warm up at idle for a bit before you start cutting. This helps protect the ignition and carburetor from thermal overload.