How did wizarding world come to know about Harry's part in what happened the day Harry's parents died?

Question

Harry Potter is well known to be the only one to survive the Killing Curse. He is famous for being the Boy who Lived, his scar is well known.

So my question is, how did it become known that he defeated Voldemort? How did it become known that he has a scar?

We have four people present that night in Godric's Hollow. James and Lily are dead. Voldemort is mostly dead, we are not sure whether at the time he knows what happened, but he is not available for questions anyway. Harry survived, but is too young to understand what happened, and too young to talk, besides nobody asks him. So why would anybody think that Voldemort cast a Killing Curse at Harry, hit him, and Harry survived that curse? How would anybody know about his scar? How would anybody know that the scar is the result of a failed Killing Curse?

Edit:
As Bellatrix below points out, it’s possible that Dumbledore could have helped spread the rumors himself. That is a reasonable assumption, because Dumbledore is usually well informed. He knew that the Potter parents were dead and that Harry lived before he sent Hagrid there, and Hagrid was there before Sirius. If it was Dumbledore, what would be his motives be?

Note that Hagrid brought Harry directly from Godric's Hollow, so the scene about the scar that Bellatrix quoted is the first time Dumbledore saw the scar.

Edit:
Radhil mentioned in a comment that Hagrid was not known to keep secrets. As Dumbledore knows Hagrid and Dumbledore sent Hagrid to fetch Harry, that means that Dumbledore knew that would happen and it was either his intention, or at least he didn't want to avoid it.

But the part of Hagrid spreading the news would only explain the information about the scar. Hagrid has no way to know what happened before he arrived.

Edit:
@TheWasp I see you changed the title, I added "about Harry's part" because that is the main focus of the question.

Answer 1

It’s unclear how the wizarding world knew about Harry’s situation.

The rumors about the Potters dying but Harry surviving began right after it happened. By then, the majority of the wizarding world already had a fairly good basic idea of what had happened that night - the Potters were killed, but Harry survived and the Dark Lord lost his powers.

“Professor McGonagall’s voice trembled as she went on. ‘That’s not all. They’re saying he tried to kill the Potters’ son, Harry. But – he couldn’t. He couldn’t kill that little boy. No one knows why, or how, but they’re saying that when he couldn’t kill Harry Potter, Voldemort’s power somehow broke – and that’s why he’s gone.”
_{^{- Harry Potter and the Philosopher's Stone, Chapter 1 (The Boy who Lived)}}

Harry was put to live with the Dursleys very soon after he got his scar. We know that Dumbledore, McGonagall, and Hagrid knew what it was and how he got it, since Dumbledore explains it to them.

“Dumbledore and Professor McGonagall bent forward over the bundle of blankets. Inside, just visible, was a baby boy, fast asleep. Under a tuft of jet-black hair over his forehead they could see a curiously shaped cut, like a bolt of lightning.

‘Is that where –?’ whispered Professor McGonagall.

‘Yes,’ said Dumbledore. ‘He’ll have that scar for ever.”
_{^{- Harry Potter and the Philosopher's Stone, Chapter 1 (The Boy who Lived)}}

However, it’s not clear how the wizarding world knew so much so quickly when there were very few people who could have told them so soon after. It’s possible that Dumbledore could have helped spread the rumors himself (if he thought the wizarding world should know), but he’d have had to do it very quickly after the Potters’ deaths and in between his trying to arrange Harry’s protection.

Answer 2

While Bellatrix’ answer is completely accurate (there is no canon information one way or another), there is one possibility which strikes me as being more likely than any other:

The rumours were likely started by residents of Godric’s Hollow, perhaps helped by Hagrid

We know that, although the Fidelius charm is very inconsistently portrayed and explained (see this previous question), the spell protecting the Potters’ house had been broken by the time Voldemort got there. Voldemort himself describes it as such in his thoughts (“and now his destination was in sight at last, the Fidelius Charm broken, though they did not know it yet”, quoted in Jeff’s answer), and as Valorum’s answer says (with spoilers), Cursed Child backs this up more explicitly.

The blast that blew up the house was, logically, loud enough to draw Muggle police, and I think it’s safe to assume it was also loud enough to draw the neighbours out into the streets. Since the Fidelius charm was broken, they could see the Potter house (or what was left of it).

We know from chapter 1 of Philosopher’s Stone that Hagrid arrived on the scene to get Harry out before the police did, but it would be very unlikely if there weren’t some neighbours there already. Dumbledore, in his wisdom, had somehow [*insert magic*] detected that something had happened chez Potters and had a damn good guess at what had happened and immediately despatched Hagrid.

So it’s almost inevitable that some local villagers (who would know that this was the Potters’ house) were at the scene to see Hagrid carrying a sleeping baby out of the rubble, quite possibly wailing about Voldemort having killed James and Lily, and very quickly started talking and sending owls from there, very efficiently starting rumours all over the country while Hagrid was flying Harry to Surrey (and whatever else he did for the rest of the 24 hours that passed between the smithereenification of the Potter house and Hagrid’s arrival in Privet Drive).

Of course, it’s also quite likely that at least one of them had contacts at the Daily Prophet or one of the wizarding radio stations and got the story to them quickly—in which case the general story would definitely be all over the country by the next morning. Whether the eyewitnesses’ accounts of what happened would be consistent enough that Harry’s part in it all could be extracted is hard to guess, but at least the basic story could get a wide audience very quickly in this way.

Answer 3

There are several factors that may have come together to provide some of the details of what had happened.

There may have been some indication that something had happened to Voldemort because people who had been under his enchantments would have been released. Hagrid notes this effect when he first tells Harry the story in Philosopher's Stone Chapter Four:

People who was on his side came back ter ours. Some of ’em came outta kinda trances. Don’ reckon they could’ve done if he was comin’ back.

So as soon as Voldemort's curse rebounded on him, there may have been dozens of people who recovered from enchantments. This would have been an immediate clue that something had happened.

We also know that it was known that Voldemort was targeting the Potters. This fact was known by at least Dumbledore, Sirius, Lupin, Pettigrew, and Snape, and possibly others. They may have arranged some sort of check-in system to constantly verify that they were still safe, and when they failed to check in it was clear that something had happened. Indeed, in Prisoner of Azkaban Chapter 17 Sirius mentions that he had arranged a check-in with Pettigrew:

I’m to blame, I know it. ... The night they died, I’d arranged to check on Peter, make sure he was still safe, but when I arrived at his hiding place, he’d gone. Yet there was no sign of a struggle. It didn’t feel right. I was scared. I set out for your parents’ house straight away. And when I saw their house, destroyed, and their bodies ... I realized what Peter must’ve done ... what I’d done. ...”

There may have also been witnesses in Godric's Hollow who saw some kind of attack/explosion and reported it.

Putting these facts together, it is certainly possible that someone would have been dispatched to the Potters house to investigate. The investigator would likely have found the dead bodies of Lily and James, and possibly the dead body of Voldemort. It would be relatively easy to surmise that Voldemort had killed Lily and James, and somehow died himself in the process. If there were no other signs of damage to the bodies that would probably be indicative of Avada Kedavra.

Additionally, an investigator might have found Voldemort's wand. A simple Prior Incantato would have revealed that Voldemort had just cast three Killing Curses. As only two people were dead, this could have indicated that Harry had survived. (Of course this could also be explained by simply saying that one of the curses missed its target.) Furthermore, an investigator might have noticed Harry's scar and guessed that that was somehow related to what had happened.

Though it does seem from the books that there was no one else there when Hagrid arrived, it is possible that someone else was sent first to see what had happened, and immediately reported back (to Dumbledore?) without doing anything at the scene of the crime.

There doesn't seem to be any evidence that the general Wizarding World knew of Voldemort's defeat before the next morning, but it is quite possible that that's how long it took for the news to spread from those in the know to the general populace.

Answer 4

The spell Morsmordre conjures the Dark Mark, and seems to be the Death Eaters as well as Lord Voldemort's calling card. The green skull practically advertises the killing curse. Did the Potters or their neighbors find it in the sky of before (to intimidate) or after the attack? Quite Likely.

Did Voldemort act alone? Maybe, but he certainly seems to prefer an audience, and it seems likely he even had the Potter's secret keeper, Peter Pettigrew, as a witness so that one finger might be left behind. Peter probably was there to lend a hand, and we all know he was quite a squealer.

Did the rebounding killing curse leave an identifiable body behind?

Do magic's like time-turners exist that would allow the ministry of magic to observe the sequence of events from a safe distance? Would the ministry have used memory stealing magic and a pensive on young Harry to see the events unfold from his perspective? Almost certainly.

How about magical speaking portraits in the homes that partially survived the attack? Unlikely, but not out of the question.

One doesn't even need to add in "Loose Lips" Hagrid or "I want you all to know" Albus. One purple plumed reporter, a few drops of veritas serum, and every wizard would know some version of the story fast enough.