[Adam]

The rule is based on the pivot foot. On a layup, there are basically two possibilities.

1. player picks up dribble with both feet in the air (most common). In this situation, the player likely picks it up just after lifting his foot. His pivot foot will be the first one to touch down. Now, he's got his pivot foot down and one foot in the air. He will then take one more step as he puts the 2nd foot down and lifts the pivot foot. This will look like the 2nd step that everyone thinks you get.
2. Player picks up dribble with one foot still on the floor. That foot is his pivot foot. Once he lifts it, he cannot put it back onto the floor before passing or shooting.
The difference between these situations is subtle, but important, as it is the difference between the player getting another step or not for a layup.

Remember, it's all about the pivot foot here.