Remove any grass or other debris that has accumulated between the blades. Grass build-up in between the blades will prevent you from being able to pull the start cord on the mower.
Check the oil on the mower to make sure that there is a sufficient amount in the engine. If the mower is low on oil it will be difficult to start and can even die after being started.
Check the battery if the mower will not start. Use a battery tester to check the battery. You can purchase a battery tester at your local hardware store or online.
Prime the engine in the right way for the conditions. Priming the engine too much or too little can lead to the engine to start and then stop suddenly or not start at all. In colder conditions the engine will require double the priming of warm weather.
Remove the grease and dirt from the carburetor with a rag. Dirty carburetors will cause the engine to idle poorly. If the carburetor is not dirty but the engine is idling unevenly, contact a professional to do an air test on the carburetor.
Check the spark plugs for corrosion and other damage. Worn out spark plugs make the engine difficult to start and cause it to die often. If the spark plugs are damaged, replace them with new ones.