So here's how it works:
Good: Works for the well being of everybody.
Neutral: Works only for his survival.
Evil: Works against the well being of everybody.
Lawful: Respects and fights for laws and order.
Neutral: Doesn't mind breaking the law but is not trying to destroy the system, only adapts to the situation.
Anarchic: Wants to break the system.
So, here are some clear examples:
Anarchic evil: Joker, Mxyzptlk - They don't care about the well being of anybody and love to break the system on purpose just to show that order doesn't work.
Neutral evil: Penguin, Clayface III - They cause a lot of mysery to other people to achieve their own well being, they don't have anything for or against the system, they just adapt to survive. Some are aware of the suffering they cause (Tobias Whale), some aren't Amygdala.
Lawful evil: Darkseid, Sinestro - They love to impose their own branch of order, which causes a lot of suffering to people. Some work within the system already, some are trying to take down the system to impose their own (terrorists or conquerors like Ra's or Starro).
Anarchic neutral: Destruction, Chemo, Titano - They use anarhy to survive, but they don't really mean to harm people.
True Neutral: Metron, Catwoman - They are strictly about their wn survival, they don't care about order or ethis either way.
Lawful neutral: Sam Lane, Morpheus - They care about order, but they don't care about the well being of other people either way. Normally soldairs fit this profile.
Lawful Good: Superman, Aquaman - They value both goodness and the established order. Sometimes they observe the order of other people (Flash), sometimes they might want to ipose their own (aquaman).
Neutral Good: Batman, Swamp Thing - They do good going with the best resource they have. They might break the law for practical purposes, but they don't hate the law.
Anarchic Good: Hitman, Guy Gardner - They work to save the day, but they don't really care about the system. Sometime they work against it because they hate it (Anarchy, V) sometimes they just find it the best method to save the day (Guy, Red Hood).