Flooded lawn mowers can happen in a variety of ways. Too much priming can saturate the inside of the cylinder; an old spark plug that doesn't fire correctly, or even old gasoline that doesn't want to burn. Any or all of those can cause a flooded engine that won't start. The best way to prevent flooding is to always use clean fresh gasoline, and always replace the spark plug once per mowing season. If you do that and the mower still floods, try this.
Grasp the spark plug wire where it meets the plug, generally called a "boot," and pull it straight off the spark plug. You may have to wiggle it a bit to get it started, and then pull firmly back and off.
Use your spark plug wrench or equivalent and push it onto the plug. The metal shell of the plug will have six sides to it, and the wrench will sit firmly around this hex metal shell. Once the wrench is in place, remove the plug by turning in a counter-clockwise direction.
Wipe off the spark plug electrode gently with your old rag. Gently is the key word here because you will be wiping off both the electrode and the tip of the plug, or the "gap" as it is called. This is where the spark happens inside of the engine and any deviation between these two may cause the mower to run rough or not at all.
Allow the hole where the spark plug was in to "air out" for about 10 minutes. You can just leave it alone, do another chore, run an errand and come back in about 10 minutes. This will allow most of the excess gasoline to evaporate inside of the flooded cylinder.
Replace the spark plug with your wrench, by first threading it into the spark plug hole with your fingers, then attaching the wrench and turning in a clockwise rotation until it is tight. Reattach the spark plug wire by grasping the boot and firmly pushing it on the end of the plug.
Place the starting position on the throttle to choke, but do not prime the engine. When an engine is primed, and most modern engines have a small rubber priming button next to the carburetor, it literally shoots a stream of gasoline directly into the cylinder. Since the engine has already been flooded, there will be plenty of gasoline residue inside, and priming won't be necessary when you get to this step. At this point, all you will need to do is put the throttle lever to choke, just as you would during a normal starting procedure, pull the starter and it should fire up.