The most important thing to consider, aside from the bowler's hand measurements, is what kind of bowling ball is being drilled. There are two basic types: Symmetrical Core balls, and Asymmetrical Core balls. Most ball companies have at least a few balls of each type. Aside from the different reaction characteristics, these balls differ in how a ball driller works to lay them out.
Symmetrical Core Balls
For symmetrical core bowling balls, the three most important factors to consider in drilling the ball are the Pin placement, Center of Gravity (CG), and the bowler's Positive Axis Point (PAP). The relationship between these three things along with the ball's surface will dictate the ball's reaction on the lane.
First, the pin placement is always taken relative to the PAP. A pin that is farther away from the PAP will tend to skid much further than a ball with a pin placed closer to the PAP. Also, a Pin placed above the finger holes will tend to go longer than one placed below them. Since the Pin controls the Track Flare, pins placed below the fingers can cause flaring over the finger and/or thumb holes. Second, the CG placement is also taken relative to the PAP. Its location will dictate the Static Weights of the bowling ball. You'll often hear balls referred to as a 4 x 4 drilling, or 5 x 3, etc. This refers to these distances. The first number is the distance in inches of the Pin to the PAP, and the second is the distance of the CG to the PAP.
Asymmetrical Core Balls
For asymmetrical core bowling balls, the only factor that changes is the CG. The CG is not used in tuning the reaction of these balls, as it is for symmetrical cores. For drilling purposes, asymmetrical balls are marked with a 3rd locator on the ball, for the Mass Bias (MB). The driller must use the pin location and MB location to get the desired reaction from an asymmetrical bowling ball. The same rules apply for the pin with regards to pin distance from the PAP as for symmetrical balls. Instead of the CG, the MB, which is always located 6 3/4" from the pin, must be measured in relation to the bowler's PAP. The MB is measured by degrees, as in a "45 degree Mass Bias". This implies that the MB is on a 45-degree angle from the bowler's PAP. As with Pin distance, the MB location affects the ball's reaction. An MB drilled at 90 degrees (closer to the thumb) will go much longer down the lane than an MB drilled at 0 degrees. The closer the MB is placed to the bowler's PAP, the earlier the roll and smoother the reaction, assuming that the Pin distance is the same.