There are two methods of making a rubber band ball. The purist will start with a rubber band bent a few times. The hobbiest will taint the ball (and get a head start) with a ball of paper. I would encourage everyone to just start with a rubber band rather than paper, it will be worth it in the end.
So buy a bag of small rubber bands and either get a ball of paper or bend a rubber band a few times. This will be the center of the ball. Now pick up a rubber band and wrap it round the ball tightly, looping the rubber band if you have to.