I would suggest using a siphon pump, which can be bought inexpensively at most auto parts and hardware stores. A good pair of petroleum resistant gloves will prevent spilling fuel on your hands when you get started.
First, grab a container to drain the bad fuel into, an old gas can would work very well. Set it on the ground next to the mower. Make sure it is below the fuel tank
Next, open up the fuel tank and put the correct side of the siphon tubing into the fuel and the other side into the container(the direction should be identified with an arrow on the siphon pump), making sure the tubing is down at the bottom of the tank.
Then pull the side of the tubing that you stuck into the container out of the container but still over the container opening. Squeeze the rubber "pump" slowly a few times. During every repetition, as you let go of the pump place a finger over the end of the tubing, making sure to remove your finger while you squeeze. It is good to have the gloves on for this.
Once it starts to pull a vacuum, your work is done. Let it continue to drain fuel until the fuel is drained from the fuel tank.
When you are done, make sure you use fresh fuel and not fuel that has been sitting in your gas can, since the fall.
If your mower had bad fuel in it, it should now start.