Internal combustion lawn mowers have been a fixture of American life since the 1940s, especially after World War II when the economy created more jobs than the labor available to fill them. Lawn mowers can literally do the yardwork that used to require several people. Manufacturers build most models to last for years of rigorous operation, so when they develop a problem, conducting most repairs is well worth the effort and expense before resorting to a new lawn mower purchase.
Find your copy of the service manual for the make and model of lawn mower. If it's gone missing, check the manufacturer's website first to see if it's available online. If not, websites like LawnAndGarden.ManualsOnline.com or RepairManual.com offer lawn mower manuals for several makes and models.
Pull the tension wire away from the spark plug, and ground it by placing it in contact with a metal surface on the engine. This will keep the lawn mower from inadvertently starting while you're working on it.
Conduct routine maintenance. Clean all surfaces of the lawn mower. Drain and replace the oil to the proper level. Check and replace the air filter, if necessary. Drain and refill the gasoline, if you haven't used the mower in awhile. Consult your manual for other recommended chores.
Identify the symptoms of the problem, if it still exists after maintenance. Some are easy: If the starter cord came off in your hand, you can stop there. Otherwise, reattach the wire to the spark plug and attempt to start the engine. Closely observe the motor function. First, does the engine start at all? If it does, does it catch? Second, will it idle? If it does, does it idle rich or lean? "Rich" refers to too much fuel in the fuel-air mixture; the engine will sputter and you'll smell unburned gasoline in the exhaust. "Lean" is just the opposite; the engine will gasp because it's not getting enough fuel. Is oil burning? A two-stroke engine burns a little oil, but a four-stroke should not. Clouds of blue smoke will be your guide. Third, if the engine itself seems to be idling fine, can it accelerate? Can it perform under load? Forth, assuming the problem is not the engine, assess how well the blades are cutting the lawn. Fifth, listen to the noise the moving parts make. Does something seem to be hitting against another surface?
Diagnose the problem. Consult your repair manual's troubleshooting section for a list of possible defects that could be causing the symptoms you've identified.
Make the repair. Follow the instructions listed in the manual for taking apart the engine to get to the affected part(s), fixing or replacing the part(s) and reassembling the lawn mower. Chances are good that one simple fix will result in more years of faithful lawn mower service.