The trick is to understand that when a fly is threatened it takes off backwards and upwards.

The two handed method is to clap behind the fly from either side of its line of flight. Notice that the hands are cupped. This way you stun the fly sufficient to kill it with a tissue, without getting fly innards on your hands.

The single handed method is to catch the fly with your hand coming towards it from the back in the direction its flight path. Once you’ve caught it, you clap your cupped hands to stun it as before.

Wash your hands afterwards and don’t try it with bees!