In most lawn mower internal combustion engines, the carburetor prepares the potent mix of air and fuel in the proportions best suited for the controlled explosion that takes place to drive the pistons downward and force the engine to turn. If there isn't enough fuel in the mix, the engine "runs lean," with not enough explosion to drive the pistons properly. When the engine "runs rich," too much fuel causes smoky operation, sputtering and flooding. Carburetors need periodic cleaning and adjustment to prevent and correct problems.
Clean the carburetor. Before adjusting the carburetor, make sure that the adjustments won't be compensating for another problem. Consult your manual on how to unseat and dismantle the carburetor, and then use a good cleaner to remove the accumulated grime.
Check for wear and make repairs as needed. Gasket kits, also known as overhaul kits and carburetor kits, for specific carburetor models are readily available online and in hardware and garden stores. Replace worn parts.
Reassemble the carburetor. For float-type carburetors, check the manual for instructions on how to adjust the float level. For diaphragm-type carburetors, read up on the metering diaphragm lever height and adjust as necessary.
Listen to how the engine runs. Start the lawnmower. If the engine will not start at all, or only with difficulty, check the fuel passages. These would include the idle mixture, fuel filter and line, throttle, choke, fuel inlet and float (on float-type carburetors) or metering level (on diaphragm-type carburetors). Consult the manual for how to make adjustments on the fuel inlet needle, throttle and choke valve that increase fuel flow. Lean operation of the engine also indicates not enough fuel. If the parts have been cleaned, the gaskets replaced and float or metering diaphragm lever correctly set, then look to the fuel filter and line, the idle mixture screw or fuel inlet needle valve.
Rich operation is indicative of a choke that won't fully open and inlet fuel needle that can't set into place, a plugged float chamber vent hole (float), diaphragm lever and metering lever issues (diaphragm) or a loose Welch plug in the fuel chamber.
Run the engine at load. If the engine can't accelerate smoothly or loses power, the fuel supply is likely being restricted. Besides the usual fuel-robbing culprits, check for air leaks between the carburetor and the intake manifold (float) or between the carburetor and the crankcase (diaphragm). Consult the manual for further clues.