What all occurs when the catcher gives the pitcher a sign.

It happens about 100-150 times a game. The catcher signals a pitch to the pitcher.
Many of those pitches occur with a runner at 1B without a runner at 2B. If that's the case, the catcher typically drops just one sign.

I'd like to discuss some of the nuances of what the pitcher ought to do, the catcher and the runner at 1B. It's very interesting.

First, let's discuss the catcher.

The catcher should first always look at the batter to make sure he isn't peaking. He can do this in some very surreptitious ways. You want to make sure his eyes are not looking rearward. The catcher then needs to just take a quick peek at the runner at 1st to check on his eyes. Does he take his eyes off the ball at all? Does he look back at the bag when he gets his lead? Does he actually try and peek in at the catcher's signals? If his eyes get off the pitcher there is a chance to record an out on a pickoff attempt.

The pitcher, in a perfect world, should not alert the runner when he is looking in for the signs. You don't want the runner at 1st to know exactly when the catcher is dropping the signal. The pitcher can avoid this by staying taller in the stretch rather than bending over and taking the sign. Astute base runners could prey on the obvious dropped signal.

The runner at 1st should get his lead in a punctual manner. Getting a delayed lead would prevent the runner from having an opportunity to steal the catcher's signals. His lead is predicated on early signals from the third base coach. When the runner has his lead and the pitcher peers in for the sign, the runner can glance in to the catcher. The runner is attempting to notice what sign has been dropped. If he can recognize off speed, he can run on it.

All of this happens in the span of 2-3 seconds. It's definitely a game within the game and it goes unnoticed more often than not.