The predominant Western table tennis grip is the Shakehand, and it is often the first grip mastered by beginning players. Ben Larcombe, a London-based table tennis coach, has a simple, accessible primer on the Shakehand grip available on his web site, “Expert Table Tennis”:
A lot of beginners try to play with two fingers on the bat, or no fingers (hammer grip). Some put their thumb up on the forehand rubber, others don’t wrap their fingers around the handle properly. Many have too big a gap between their hand and the top of the handle. I always emphasise that you should ‘shuffle/slide’ your hand up the handle until it reaches the top and then hold that grip loosely.
If you play in the Western world, chances are you will be exposed to mostly Shakehand players. It’s a powerful, simple grip with a easy switch from fore- to backhand play.