How did Dumbldore AND Voldemort know?

Err... Well, Dumbledore can figure out pretty much anything, and Voldemort experienced it firsthand more than once, didn't he?
They're both smart, and could have put two and two together...

I think they both chose to believe a theory that Lily had generated a magical sacrificial protection in order to explain why Harry survived an Avada Kedavra...

They probobly just.. knew, as all the other things Dumbledore knew..
however, there are just too many deaths and sacrifaces for that theory to sound logical, even a bit

I think its quite obvius... They knew that hersacrifice saved him because there isn't any otherway to survive a killing curse,no mather how stong are your magical powers...
That's how they know... Or thats what I think..

Well, no one ever said the magical protection was SOLELY based on Lily's sacrifice. I mean, if she was something of the Marauder's Hermione- it's not much of a stretch to think that she could have evoked some powerful charm or rune or potion, whatever, that would be triggered by the ultimate sacrifice? Some ancient and obscure spell, perhaps, though certainly recognizable to such minds and skills as Dumbledore and Voldemort.

The reason that it is not commonly used- simple- it's not commonly known. And furthermore, only applicable under the most dire of situations- not something most people prepare for constantly.

Another possibility- Lily was the only one who discovered while researching, or in some very old book, or whatever- so,
1)she told Dumbledore
2)Voldemort DIDNT know about it- but he encountered its resistance (it seems unlikely he never even tested the wards on the Dursleys) and thus figured out exactly what had happened.

Also maybe something to do with fact that both are perhaps the most accomplished and powerful Legilimancy users.

JKR explained this. It was because Voldemort gave Lily a choice, which he had never really done before. So even though, say, James also sacrificed himself, that didn't evoke a magical protection because Voldemort would have killed him anyway.
But Lily could have run and saved herself, which she refused to do, and so her choice to die to try to save Harry is what caused the protection.

Very well said!!

Thats it, exactly! Her choice to die for Harry is what did it.
In the aftermath & Harry's survival, it was probably the only conclusion that Dumbledore could come to.....
As for Voldemort, he didnt consider love to be a powerful magical force, he was obviously sorely mistaken.....

indeed. For that to happen..he would need to know what it feels like. And he never did, so in a way...he was never really human...coz in a way...to be human is to love.