Modern swordsmithing seems to make use of drilling and boring the Pommel and handle to fit the tang. But drill presses didn't exist in those days. How was a sword's handle (and pommel) attached to a tang, and made sturdy?
One technique used to hold the assembly together is called 'peening'. The tang actually penetrates through the end of the pommel, and then is hammered and polished flush. The (commercial) website Albion Swords has some excellent diagrams displaying this and other methods. A google image search on 'sword peening pommel' will also give you some sample images of what this method looks like.
In some cases the grips were actually hollowed out to slide over the tang, then held in place by the (peened) pommel. Other grip styles often involved rings of material slid over the tang, or leather and wire wrapped around it. Again a search will show many samples of this online.
Concerning the actual hole through the pommel itself, it again depends on the material involved. If the material is forgeable, then punches or more specialized custom tools can be pushed through the red-hot pommel. Castable items might use molds with the penetration already included. A discussion here talks about some of these tools and techniques.
The processes are fascinating, and there are many youtube videos showing the forging/creation of medieval style weapons. A Discovery Channel 'How its Made' video can be seen here which shows some of these methods (peening and casting the pommel). A Nova special on Viking Ulfberht swords is also great for gaining an understanding of some of the procedures.