Place the handkerchief in the cup, pushing it all the way down
to the bottom. Invert the cup and push the cup under water (completely).
Bring the cup back up and pull the hankerchief out - it should
be still dry.
As you push the cup under water
you catch a pocket of air in the cup. It cannot escape unless
you tilt the cup (because air is lighter than water and therefore
can only travel up - but it is blocked by the cup). The further
down you push the cup, the more the water will compress the
air and it will therefore slowly approach the handkerchief the deeper you go.