My predecessor David Landry wrote this back in 2006. It is a very good tutorial in how catchers give signs and how they affect the game. The top catchers in MLB like Yadier Molina of the St. Louis Cardinals and Carlos Ruiz of the Philadelphia Phillies are prized not just for their overall defense and offensive contributions, but especially how they "call the game".

I'm in Ireland celebrating my wife's birthday this week so see you soon!
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The catcher is much more than a human backstop. He is typically responsible for directing the entire defense from his position behind home plate. The better catchers are even responsible for “calling the game”. Calling the game requires the catcher to study and know the tendencies of all opposing batters and those of the pitcher. He uses this knowledge to select the appropriate pitch. The pitch is relayed to the pitcher using a sign.

Signs
Signs are hand and arm signals that are determined in advance of the game. All pitchers and catchers must be know the signs in effect for each game. For example, the signs may be one finger for fast ball, two for curve, three for slider and fingers shaking for a change-up. The sign frequently also indicates the intended pitch location, such as low and inside. There may be a different set of signs for positioning the infield.

Stealing Signs
Opposing teams will try to steal signs. The best opportunity to do this occurs when there is a runner at second base. The runner at second has the best view of the catcher and is in an excellent position to relay information to the catcher through signs of his own.

Protecting the Signs
The first rule of signs is that the catcher needs to make sure the opposing team doesn’t steal the signs. To do this, he shields the hand making the sign between his knee and the catcher’s mitt. This ensures that coaches and runners at first and third can’t see the sign.

Changing Signs
If the catcher suspects the signs have been stolen, he will change the signs. He might do this by adjusting his mask in a particular manner or by some repetition of finger signals like one finger followed by a fist. With changed signs, one finger might become curve instead of fast ball.

The Set Up
The sign not only tells the pitcher which pitch to throw, it determines how the catcher “sets up”. The set-up is the glove placement and body positioning by the catcher. If a catcher sets up for a fastball low and inside, but the pitcher throws it high and outside, there’s a risk of a past ball.

The Mound Conference
When the catcher determines that the pitcher is confused about the signs, he will call time out and walk to the mound. Again, secrecy is important. To protect against lip readers, the pitcher and catcher will talk with their gloves in front of their mouths. This is probably overkill, but the practice is almost universal in MLB.