Bunting is holding the bat out to tap the ball without swinging the bat. The idea is to hit the ball a short distance causing the pitcher or third baseman to have to field the ball.
When to Bunt
Sacrifice - Bunting is most often used as a sacrifice play. This is when a player bunts to move a base runner from first to second or second to third. The intent is that the batter will be thrown out at first "sacrificing" himself in order for the base runner to move closer to home.
Squeeze play - This is a sacrifice bunt with the runner on third base. A suicide squeeze play is when the runner from third base takes off as the pitch is thrown counting on the player bunting to make contact with the ball. If the bunter misses, the runner will almost surely be out.
Base hit - A bunt can also be used to try and get a base hit. This is generally attempted by a fast player when the third baseman is playing deep.
How to Hold the Bat
For a right handed batter, move your right hand about a third of the way up the bat. To keep your hand from getting hit by the ball you can hold the bat between your index finger and your thumb. If you feel comfortable that you won't hit your hand, you can grip the bat putting your fingers and thumb around the bat. This will give you more control of the bat.
Hold the bat out in front of your body and angled up slightly.
How to Stand
As the pitcher prepares to pitch, turn and face the pitcher with the bat up in the strike zone. You want to start the bat high in the strike zone so you can move the bat down to hit it. Your shoulders will be square with the pitcher. Start out with your knees bent slightly.
Striking the Ball
Just like with hitting, you need to concentrate on the ball. It's easy to take your eye off of the ball to watch the base runner, the pitcher, or the third baseman. However, you must watch the ball all the way to the bat. As the ball approaches bend your knees to match the height of the pitch.
Next, you want to let the ball strike the bat, not the other way around. Deflect the ball towards third base. This will give you the most time and the best chance to reach first base safely. In some cases you may want to bunt the ball towards the first baseman.