You need to find out what the spindle taper of the drill press is. It'll probably be either a female Morse taper or a male Jacobs taper.
If your drill press spindle has a Morse taper, you'll need an adapter to go from the female Morse on the drill press to the female Jacobs in the back end up the Tapmatic.
If your drill press spindle has a Jacobs taper, find out which one it is (it's probably printed/etched on the drill chuck) and find a Tapmatic with the same size taper in it.
If you've never seen one of these mating tapers, you won't believe they work. The male side is a smooth metal cone and the female side is a hole which perfectly matches it. If both are nice and clean, you simply fit them together and knock them together with a hammer (put a piece of wood or plastic in the way of the hammer to avoid messing anything up).
-Allin