Small gasoline Engines require 3 things. Spark, compression and fuel. And chainsaw need 2-cycle oil mixed with the gas.

Assuming you have the right oil-gas mixture and a fresh batch of gas, and you didn't leave old gas in the saw all summer long since last November.

-Take off the dirty air filter and see if saw starts without filter. Do not run without putting in new filter.
-Check exhaust port for mud dobber home or screen clogged with carbon and dirt
-See if saw fires up after squirting WD-40 directly into carburetor
-Check gas line >>> pull gas line loose and see if gas flows out of tank to carburetor
-Take out spark plug > put finger over spark hole and pull cord >> do you feel suction that says you got compression?
-Put spark wire back on spark plug >>> hold spark plug so threads touch bare metal part of spark plug hole >>> pull starter cord and see if spark shows between plug and saw >>> suggest you not hold metal part of spark plug while pulling cord [you'll understand why]
-If spark plug shows spark, then your saw has spark ... so put in new plug and start fresh.

If your saw has compression, spark, and fuel it should start unless carburetor is gummed up because gas was left in tank.
Here is the final trick. Start the saw while spraying WD-40 directly into carburetor and see if you can keep it going with the WD-40. This might take a helper. If this does not work, then carburetor is bad or gas line is clogged at carburetor. Time to take it to the shop.