If the pull cord on your lawn mower is operating correctly, gas is flowing, the spark plug is working, and there is sufficient air in the carburetor, it shouldn't take more than four to six pulls to get it going. Lawn mowers are typically hardest to start in the spring after being in storage for several months, but poor maintenance practices and damp weather can make starting difficult any time of year.
After a long winter, or after 100 or more service hours, the electrode on the spark plug can get contaminated and won't spark properly when you pull the starting cord. In damp weather, the electrodes may be covered with moisture, and if the mower is old enough, oil may be blowing into the combustion chamber and collecting on the plug. It's easy to remove the plug and check. You can often clean the electrodes with a rag and a file to restore the spark, but excessive black carbon deposits signify an air flow problem.
Restricted Air Flow
Carbon deposits on the plug are normal, but thick black ones that interfere with the plug's ability to spark signify a deficiency of air in the combustion chamber. When there isn't enough air, the fuel burns inefficiently, and the mower smokes during operation. The lack of air is crucial when you're trying to start the engine, because without air, the fuel can't ignite -- even if there is a spark. Restricted air flow is easy to remedy: Simply change, clean or replace the air filter, and if the mower has a spark arrester, clean it with a wire brush.
If you stored the mower for an extended period with fuel in the tank and forgot to add stabilizer, the fuel may be stale. This happens because moisture settles in the gas tank, sinks to the bottom, and combines with the gas to form a thick varnish that clogs the carburetor and fuel lines. Once the engine starts, the movement of fuel may dissolve these deposits, but to get it to turn over, you'll probably have to drain the old fuel and replace it. After you do that, remove the air filter and spray cleaning fluid into the carburetor before pulling the starter rope.
Correct Starting Procedure
Even with proper fuel, plenty of air, and a clean plug, you can have trouble starting your lawn mower if you don't use the correct starting procedure. Many mowers have an on-off switch, and that switch must be on. If your mower has a priming bulb, you should depress it the recommended number of times -- usually between four and seven -- before pulling the starting rope. It's important to use the choke correctly if your mower has one. Close it completely, but if the mower doesn't turn over after the first four pulls, open it halfway before the fifth pull. Failure to do this usually results in engine flooding.