In general, problems with mowers are either due to lack of a spark or fuel blockages.
Check the cable going to the spark plug is making good contact and that you are actually getting a spark when the plug is held against the body of the mower and the starter rope is pulled (you might need an assistant to stop the plug bouncing about. Make sure they don't touch the cable!)
Check the vent in the fuel cap isn't blocked.
If the carburettor has a float bowl, sometimes the valve allowing entry of fuel into the bowl becomes blocked by debris. Turn off the fuel tap and remove the bowl (It will be held on by a bolt, or couple of screws) while holding a jar underneath to collect any fuel. Turn on the tap and check fuel flows freely. Remove any debris from the bowl and replace.
If the tank is located below the carburettor, fuel is pumped from the tank up into a small reservoir with a weir which allows to flow back into the tank. This reservoir keeps the fuel level constant, independent of the fuel level in the tank. There are mesh type fuel filters on the tubes which suck fuel from the tank to the reservoir and reservoir to carburettor venturi and these can become coated with dirt.
Check also that there is nothing causing the kill switch (which cuts the power when you switch the mower off) to operate. This may be located near the throttle cable at the carburettor or under the cowling which covers the flywheel.
You can check out my troubleshooting article about lawnmower problems on HubPages at
http://eugbug.hubpages.com/hub/Why-Wont-That-Lawnmower-Start
Euge, January 2013
