You will need:
There are areas of the balloon which are more stretched than others.
If you try to pierce the balloon from the side, i.e. where it is most stretched, the balloon rubber will tear itself apart due to the elastic tension over the rubber. Piercing the bottom of the balloon is best place; the rubber has less elastic tension and the rubber itself will grip onto the skewer due to friction.
This is a great way to show that science can be found in sorts of places, even in sideshow acts where a magician uses 'magic' to get a skewer through a balloon.
Other friction experiment: Suspended rice bottle