If a lawnmower refuses to start, the problem is generally with the fuel mix or the carburetor. Check the fuel tank for fuel, and refill it if necessary, then check the air filter to see if it needs cleaning or replacement.
If the mower has a float bowl, loosen the bolt on the bottom of the bowl and then the bowl itself. Gasoline should drip from the loosened bowl; if it does not, check the fuel filter and the fuel line to ensure that gas is passing through them. If gas is reaching the float bowl, clean the carburetor main jet using commercially available carb cleaner. If the mower starts but runs rough, rebuild or replace the carburetor.