Alignment is not as easy as it sounds, since the old days of D&D, it was a very important trait a character had. In some editions (like 3e) there were plenty of rules about what spells subjects you to what degree depending on your alignment, what magic weapon you could use, etc. In 3e especially you were punished for having an alignment other than neutral and double punished for not having any neutral in your alignment. Pathfinder, too.
In 4e alignments were reduced from nine to five, since some alignments are somewhat difficult to actually pull off and so some harder borderlines were combined. So a chaotic good character would be a ‘good’ character, since the anarchy of chaos don’t mash well with the good component. Chaotic neutral is in most cases chaotic evil either way, and so on.
In 5e we’re back to 9, or more precisely 10, since a creature can be unaligned, which means that there is not enough intelligence or self-awareness to actually have a proper understanding of morality. And here we come to the core of alignments, they’re the morality compass! Which means that whenever a character have problems in solving a dilemma of morals, he’d lean towards his alignment. Would he rather give in the demands of the bandits, who keeps hostages or start a bold maneuver in hope to keep them all save? Both would be good-natured but to not risk the hostages is a more lawful way of thinking, while chaotic characters takes more chances.
But sometimes it can be hard to actually choose an alignment and the PHB and Base Rules doesn’t offer much help and some descriptions aren’t good advertisement for their respective alignments, like ‘Lawful Good (LG) creatures can be counted on to do the right thing as expected by society’. Even though it’s completely right, the ‘society’-part is kinda repulsive for most players at first sight. Because they want their characters to be exceptional beings, which are able to sh*t on society, if needed.
So I thought I’ll just explain how I handle it in my campaigns, which are my personal attributes each alignment extreme have.
Good: To be a good character, one thing is not required: To say that all you do is for the good. Most of those who says it are evil anyway. If I need a personality trait which defines a good character, it would be: You’re helping others even if it doesn’t benefit you and might get you in danger! Or in one word: Selflessness.
If you act out of kindness, feels sympathy to the suffering and doesn’t think of rewards when helping people, than you’re definitely a good character.
Evil: When good characters are selfless, evils are logically selfish. When a character is mostly about having the best comfort, use any shortcut and easy way you find and doesn’t care much about others, than said character is most likely evil. Those who are power-ridden, use any means necessary for their goals (even though they happen to be good) and only truly respects themselves, are about to fall into the evil alignments. Greed is a source for evilness, too.
So if your character doesn’t actually feel any compassion and always says “It’s just an orc” and other excuses, while only looking into what his/her reward is, that character is evil.
Lawful: A lawful character is someone who wants to give to and take from society. He has a stable set of rules, tries to minimize risks at all cost and keep thinking about the greater picture. Order is important, since when things are orderly, you can make your decisions with less error rate. You acknowledge laws by themselves, even though you don’t need to agree with them yourself, but at least you have a decent amount of rules, be it by your own society or by yourself. And you stick with your rules!
If you’re playing a character who think things normally through, shows a decent amount of self-discipline and play by certain rules your character acknowledges, he is most likely a lawful character.
Chaotic: The character has wimps and goes with them at any opportunity he faces problems or sometimes even discomfort. An chaotic character have himself under much less control, so he tends to impulsive and sometimes irrational actions, often fueled by his good/evil awareness. The character will simply infringe laws if needed and think more about his own surrounding and emotions, be they selfless or selfish.
If your character is moody, screw the rules repetitively, is more short-sighted and have a lack of self-control, all points to a chaotic alignment. A more tempered way to say it is: He’s thinking with his heart and disregarding his head at times.
Neutral: Neutral is always a balance-act, since it means to be neither the one or the other. If someone tries to keep balance between good and evil it means, he/she’s good if he/she can and evil, if he/she must. If the character is neutral on the order/chaos-axis, this means that he will neither go with every wimp nor restrict himself as much as a lawful character would do. A true neutral character would seek balance in every possible aspect, being an extreme by himself/herself.
Of course these are my personal impressions, but if you start to combine those angles, you get imo a somehow accurate picture. It’s not entirely perfect, but after explaining these, I can even get my players to grasp the difference between chaotic evil and chaotic neutral (which is a difference even a lot of experienced players have trouble in seeing).
But if that’s not sufficient, take nederbird’s alignment chart. It’s also decent, even though I’d personally disagree here and there. 😉