Alignment is one of the most difficult mechanics of D&D game, if not THE most difficult.
Pages in manuals, which were written by designers to define how really alignments do work, are numberless, as well as Dragon articles or posts on forums and blogs.
As written in a previous post, Wizard has solved the problem by letting smaller space to alignment and introducing concepts like Bond, Ideal and Flaw.
The only really important rule about alignment is
Don't ever tell a PC "you can't do that (or 'you must do that') because you're restrained (or 'you're obliged') by your alignment"
Alignment is part of the moral sphere of men (or every other playable race in D&D) and then, like every other part, is an extremely subjective thing and then extremely various from one man to another.
Let's see how a man could be considered with different alignments by his own actions.
Take the main character of the movie Carlito's Way, the gangster Carlito (Charlie) Brigante, with Al Pacino as actor.
It's obviously a criminal; he has killed, robbed, been in drugs dealings, and he will do the same things in the movie. We can easily define him as Chaotic, since he has made a lot of crimes.
He has a good side too: he believes in friendship ( he helps many times friends in need), he truly loves a woman ( he'll die for her) and he has't never betrayed his fellow mobsters and his boss.
So we may think about him as a Chaotic Good character.
But now let's think about him once again.
He has an own personal code of conduct, which he strictly follows even if in doing so it means bad consequences for him ( his woman once says " you and your damned hood's code of honor") and this behaviour is typically Lawful.
But Carlito is also a ruthless killer who doesn't hesitate to kill everyone who's an obstacle to his plan ( to have a better life ) and for vengeance he's going to kill even his friends.
So he can be viewed as a Lawful Evil character too.
We have just seen how a character, according to his own same actions, can at the same time be two different alignments, which are at the opposite sides of the axis.
Then, as a Rule of the Good DM
Don't think about alignments as a group of prohibition. They're simply an useful tool which helps you to give a better depth to your characters.
However, if you feel they are too difficult to use or if to give a deeper insight is not your goal, don't use alignments.
You'll enjoy the game even without them.