There is no “official” alignment system for Swords & Wizardry. In some campaigns, the struggle between Law and Chaos is the only supernatural conflict, and Good and Evil are nothing more than personal preferences held by mortals (theSword & Sorcery model). In other campaigns, it is the struggle between Good and Evil that defines where gods and mortals stand in the grand scheme of events (the High Fantasy model).
Some campaigns might contain supernatural factions backing the whole set of Law, Chaos, Good, Evil, Neutrality, or mixtures of the various alignments. These core rules don’t try to tell the Referee how to handle alignment; the Referee is free to use any system he chooses. If you’re playing the game and you want an “unofficial” default, then the players may choose one of three alignments: Law, Chaos, or Neutrality. Most characters will be neutral. The good guys are Lawful, the bad guys are Chaotic, and anyone just trying to achieve fame and fortune is Neutral.
Good and Evil are not mere philosophical concepts in the campaign world, but are actual sentient forces battling for dominion. Also in eternal conflict, and often acting in concert with Good and Evil (though allied to neither in particular), are the forces of Law and of Chaos.
As a rough guide to the general tenets of the alignments:
Characters need not be formally aligned with any of these forces. If they are, however, they gain certain benefits and obligations from that alliance. Specifically, they are then required to act in a way which furthers the aims of their patron alignment, which may enforce certain behaviours.
Note that this has little to do with an individual's personal morals or philosophy. It would be quite conceivable for a psychotic baby-torturer to be Good aligned (assuming such an alignment served the individual's purposes). As long as he or she acted in a fashion which didn't void the alignment, all the benefits of that alignment accrue to them. Even if they daydream of ravishing and murdering virgin halfling slaves, as long as they don't act on those desires — in any way, including allowing or encouraging others to do so — then they are, for the purposes of alignment, Good.
Since this example would require an evil person to act in every way as if he or she were good, the net effect is the same as if they truly were good right to the centre of their soul. Motivation is not an issue in formal alignment.
Alignment is (initially) a conscious choice, but once the choice is made, there is no turning back. An aligned character is a soldier in the eternal conflict between Good and Evil, Law and Chaos, and they are not merciful powers when it comes to backsliders. Once aligned, always aligned, one way or another. If you once enter the game, you remain in the game until you die — and sometimes afterwards.
A character can change alignments, either as a conscious choice, by actions which persistently violate the original alignment code, or involuntarily by magical means. The residue of the old alignment will take time to fade, however, and followers of the old alignment are unlikely to be forgiving if they find out that they are dealing with a turncoat. A formerly aligned character who attempts to become Neutral will find that they now have enemies on every side. Neutrality is seldom more than a temporary, transitional state in such cases.
True Neutrals are those who have never been aligned in any way. In terms of the Great Game, they are more or less ignored. They are merely natural hazards to be avoided or overcome, or potential tools to be used and discarded.
Note: Almost all characters, whether PC or NPC, will be formally aligned one way or another. Very few ordinary people will be. The very act of aligning declares willingness to be seen as a Player, with all the benefits and dangers that entails.