Handle the needles so some of the oil from your skin rubs off onto the needles. The oil helps the needle stay dry by repelling water. Be cautious when you get near the sharp tip. Do not get the needles wet.
Magnetize one of the needles by repeatedly stroking the needle in the same direction with one pole of a magnet. You are making the needle into a magnet. After inducing magnetism, place the magnet away from the experiment area.
Hold the needle horizontally around its middle between two fingers. Lower the needle until it is close to the surface of the water, open your fingers and let it go. It might take multiple tries to get a needle to float. If it sinks, remove it from the water, put it on the paper towel and magnetize another needle.
Watch the needle orient itself so the ends face north and south. If you check the needle's accuracy with a compass, keep the compass away from the needle so their magnetic fields do not interact. The water molecules attract each other electrically, and through surface tension, form a kind of stretchy skin. The magnetized needle floats on this "skin" the same way an insect called a water strider walks on the surface of the water.