The most basic way to hold a bowling ball is called the conventional bowling grip. This is a very important thing to know while browsing the racks of bowling balls at your local bowling center.
There are three holes in a typical bowling ball. Two are side by side and one, usually the largest of the three, below those two. Put your middle finger and ring finger in the side-by-side holes and your thumb in the other. This grip gives you the most control and lowest likelihood for a freak injury.
Finding the Right Fit
With a house ball, the size of the holes don't really matter, as long as they're big enough to fit your fingers. You don't want them too tight. You also don't want them too loose, although that won't be much of an issue if the holes are the right distance apart.
First, put your thumb all the way into the thumb hole. Lay your middle and ring fingers over the finger holes. If your second knuckle (from the top) is over the middle of the holes, you found a good fit.
Hold the Ball for Bowling
While bowling, you should hold the ball as shown in the image on this page. To create that grip, first put your thumb all the way into the thumb hole, as you did while selecting a ball. Then, insert your middle and ring fingers into the other holes. The ball should feel secure in your hand.