Spread a rag under the mower (it’s best to do this outside, where the ventilation will be better). Make sure you take safety precautions, including making use of safety glasses and gloves, and have some kitty litter handy as a quick-dry for spills.
Take off the gas cap and use an old rag to wipe out the inside of the filler.
Put a siphon hose from the fuel tank to a gas can on the ground and squeeze the bulb enough times to produce a vacuum that will begin draining gas from the fuel tank to the can.
Drain as much as you can from the tank with the siphon hose.
Next, take a look at the carburetor and see if it has a drainage bolt on the bottom of the float tank.
Where possible, remove this drainage bolt and let the fuel run out of the float tank. Then, take out the entire carburetor.
Spray the bore, choke, and any other accessible components of the carburetor with aerosol carburetor cleaner and remount it on the engine.
Reassemble all components and start the engine. You may have to spray starting fluid in the carburetor’s bore to get it running again. With any luck, you should be set to go again for another season of mowing and yard work.