Alignment is a shorthand description of a complex moral code. It sketches out the basic attitudes of a person, place, or thing. It is a tool for the DM. In sudden or surprising situations, it guides the DM's evaluation of NPC or creature reactions. By implication, it predicts the types of laws and enforcement found in a given area. It affects the use of certain highly specialized magical items.
For all the things alignment is, there are some very important things that it is not. It is not a hammer to pound over the heads of player characters who misbehave. It is not a code of behavior carved in stone. It is not absolute, but it can vary from place to place. Neither should alignment be confused with personality. It shapes personality, but there is more to a person than just alignment.
Player Character Alignment
It is essential that each character's alignment be noted in the DM's records for that character. Are the alignments too different? Are they different enough to break the party apart? Will this interfere with the planned adventure or campaign?
Sometimes characters of different alignments possess such radically varied world views to make cooperation impossible. For example, a strict lawful good and a chaotic neutral would find their adventuring marked by animosity and mistrust. A true chaotic neutral would make just about anyone trying to work with him crazy.
There are two approaches to an alignment problem in the group. The first is to explain the problem to the players involved. Explain why their alignments could cause problems and see if they agree or disagree. If necessary, suggest some alignment changes—but never force a player to choose a new alignment.
It is his character, after all. Wildly different characters might find ways to work together, making adventures amusing (at least) and maybe even successful in spite of the group's problems.
The second approach requires that players keep their alignments secret. Don't tell anyone that there might be a problem. Let players role-play their characters and discover the problems on their own. When problems arise, let the characters work them out themselves. This approach is best suited to experienced role-players, and even then it can play havoc with a campaign. Since secrecy implies mistrust, this method should be used with extreme caution.
During play, pay attention to the actions of the player characters. Occasionally compare these against the characters' alignments. Note instances in which the character acted against the principles of his alignment. Watch for tendencies to drift toward another, specific alignment.
If a character's class requires that he adhere to a specific alignment, caution him when a proposed action seems contrary to that alignment. Allow the player to reconsider.
Never tell a player that his character cannot do something because of his alignment. Player characters are controlled by the players. The DM intervenes only in rare cases (when the character is controlled by a spell or magical item, for example).
Finally as in all points of disagreement with your players, listen to their arguments when your understanding of an alignment differs from theirs. Even though you go to great effort in preparing your game, the campaign world is not yours alone—it also belongs to your players.