I'll try to make this as spoiler-free as possible, but dialogue choices will be mentioned so it is impossible to explain in a completely spoiler-free manner. Read at your own risk.

​Also, the names and choices listed are made from a mix of my hazy memory of the context of the conversations and what little info I could get from the current Koei-Tecmo EU site's screenshots on names. Some wording (especially on dialogue choices) may differ from the NA/EU version slightly. Use your common sense and match them up, and feel free to leave comments once the game is out if you'd like to let me know what the actual wording is for the choices in the English version.
Nights of Azure has 5 total endings, separated into 3 main types - three 'Normal' endings (let's call them N1, N2, N3), one 'True' ending, and one 'Bonus' ending.

The first ending you see will be one of the 'Normal' ending variations, N1, N2, or N3. Which one you see depends on Arnice's affection level with Lilysse. Low affection will end with N1, medium affection with N2, high with N3. You shouldn't worry too much if you mess up, and certainly shouldn't restart your game. Read about the True and Extra endings to see why your first ending doesn't matter that much!

In order to get the highest affection level you can, you should make sure to fulfill Lilysse's requests in the letters she leaves on the Hotel Ende counter without fail (she will leave a new request in Chapters 1, 2, 4, 5, and 7, and also to make the right dialogue choices at certain points. I don't think you need to hit ALL of these, but grab as many as you can if you want N3 your first time.

O = Correct
X = Incorrect

The Choices :
Chapter 1: Talking with the Maiden of Jorth, she will offer to answer just one question.
O : About your relationship with Lilysse
X : About the identity of the Maiden of Jorth

Chapter 2: Talking with Dream Lilysse, she offers to answer a question.
X : About the First Saint's sealing of the Nightlord
O : About Lilysse's feelings

When Arnice hits Level 4, talking with the Maiden of Jorth.
O : About how the Saint is chosen
X : About how Agents are chosen

When Arnice hits Level 5, talking with the Maiden of Jorth.
X : Request Lilysse's blood
O : Refuse the proposal

When Arnice hits Level 6, talking with the Maiden of Jorth.
O : About the Saint's seal
X : About the everlasting night

When Arnice hits Level 8, talking with the Maiden of Jorth.
O : Dispose of it
X : Maintain it

When Arnice hits Level 11, talking with the Maiden of Jorth.
O : Lilysse
X : The Nightlord

The last Level 11 choice is included just for completeness sake of all dialogue options that raise affection with Lilysse, you do NOT need it to get N3 ending. By the time you're Lv.11 you'll be well past the normal endings anyway.

Only attainable after you've cleared the main game. Save your game after you beat the main scenario, and load the save data to continue into the postgame scenarios.

Clear all the postgame Extra Scenario events (every scenario except for 'The Last Night' should be marked Complete).

Arnice's affection level with Lilysse doesn't matter at all! Even if you got the worst Normal ending earlier, you'll still get the True End this time.

Face the end boss again with all the postgame scenarios complete, and you'll get the True End. That's all there is to it. Easy, right?

After getting the True Ending, if you continue playing from that save data, you'll be able to visit the Altar of Jorth and freely change Arnice's affection level with Lilysse! Yes, this means that all the trouble you went to earlier to fulfill her requests and choose the right dialogue didn't matter if you were patient enough to play this long, because now you can choose from five different affection levels freely and then go beat the boss again to get that affection level's corresponding ending at any time.

There are five affection levels you can freely switch between at the Altar of Jorth. The lowest three will give you N1, N2, N3 normal endings. The second highest will give you the True End. And the new, additional highest one will give you a bonus ending. Set the affection level to highest and go beat the end boss again to see the bonus end.

N1 : It's just okay.
N2 : It's good.
N3 : It's very good.
True Ending : It's great.
Bonus Ending : It may be too good to be true...

Credit to JRPG Review[www.jrpgreview.com] for the guide English version and ds-can's wiki[ds-can.com] for the Japanese version of the game for the info.