There is a common misconception about bridge pins. That is that they are meant to hold the strings in the bridge. They are not. Something under tension cannot be anchored with something that is mobile.
The ball end of the string should come to rest on the bridge plate. The bridge plate is a piece of wood, usually spruce, that is glued under the top directly below the bridge. It reinforces the top to minimize the hump caused by the bridge being in rotation from the pull of the strings. It also serves as a mounting surface for the ball end of the string.
Put the string through the hole in the bridge. Place your hand through the sound hole. Reach down and find the ball end. bend it slightly while installing the bridge pin, making sure that it is contact with the plate rather than the bottom of the pin. Install the end of the string and tune. Repeat with the other strings.
Some folks feel that doing this correctly will increase the tone and volume of the guitar.
On a side note, incorrectly installing the strings so that the ball end is at the bottom of the pin is the major reason for bridges splitting through the pin holes. A bridge pin is a conical wedge. Repeated pushing and hammering them into place in an attempt to use friction to hold the end of the string results in splitting the bridge as neatly as using a wedge when splitting logs.
