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So all wizards get an invitation to Hogwarts at 11... How do they know whom to invite?

If a wizard is Muggle-born, then nobody would know about their existence.

Or do they register some weird magical stuff being done by them before 11?

Kevin
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Jana
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    I started to ask this very question. I believe some Muggle born Witches/Wizards escape the Wizarding Worlds attention, grow up untrained, and become magicians. – Major Stackings Aug 28 '14 at 06:21

3 Answers3

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As per JKR, there's a way (and it's McGonagall, not Dumbledore, who finds out for some reason)

... Also how does the Ministry of Magic find out these kids have powers?
... JKR. The Ministry of Magic doesn't find out which children are magic. In Hogwarts there's a magical quill which detects the birth of a magical child, and writes his or her name down in a large parchment book. Every year Professor McGonagall checks the book, and sends owls to the people who are turning 11.
(source: Online chat transcript, Scholastic.com, 3 February 2000)

DVK-on-Ahch-To
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    I believe Hermione tells Harry and Ron about the quill in the books too. – Kevin Feb 05 '12 at 17:18
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    @Kevin - I don't recall that... do you have a quote or approximate circumstances? If so you should make it into an asnwer. – DVK-on-Ahch-To Feb 05 '12 at 17:36
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    @Kevin: The closest I can find at the moment is Hagrid telling Uncle Vernon "His name's been down ever since he was born" in the 1st book, Chapter 4. – Hendrik Vogt Feb 14 '12 at 17:42
  • @HendrikVogt Yeah, I think I must be recalling my sister telling me, she follows all the extra JKR stuff. – Kevin Feb 14 '12 at 17:59
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    ...Wait, what about children who go to completely different magical schools? – Zibbobz May 01 '14 at 14:35
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    @Zibbobz: if they live in Great Britain or Ireland, their name is written in the book too, but nobody is required to attend Hogwarts. If they live outside, they do not get invited, for Hogwarts is a Britain-only school. – b_jonas Jun 29 '14 at 21:26
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Whenever a magical child is born, a magical quill writes that child's name down in a ledger of sorts. When the child turns eleven, he/she is sent a Hogwarts letter. There is no canon information regarding the other Wizarding schools, such as Beauxbatons or Durmstrang. Scholastic Chat 02.03.00

Slytherincess
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    cool! 2 answers in 5 mins! I'll accept the one with the JKR quote, but +1 for this one as well! – Jana Feb 05 '12 at 12:47
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In addition to the two existing answers, there’s some Pottermore sample content which goes into more detail. It’s titled the Quill of Acceptance and the Book of Admittance (no account required). It starts as follows:

In a small locked tower, never visited by any student at Hogwarts, sits an ancient book that has not been touched by human hands since the four founders placed it there on completion of the castle. Beside the book, which is bound in peeling black dragon-hide, stands a small silver inkpot and from this protrudes a long, faded quill. These are the Quill of Acceptance and the Book of Admittance and they constitute the only process by which students are selected for Hogwarts School of Witchcraft and Wizardry.

Essentially, the Quill and the Book are somehow able to detect signs of magic in young children, and their names are recorded in the book, without human intervention:

At the precise moment that a child first exhibits signs of magic, the Quill, which is believed to have been taken from an Augurey, floats up out of its inkpot and attempts to inscribe the name of that child upon the pages of the Book.

The Pottermore content also explains that the mechanism behind the Quill and Book are entirely secret (to avoid arguments with disgruntled parents), and how this system ensures Squibs aren’t admitted by accident. I recommend reading it in full.

Then, as per the interview cited in the other two answers, the admissions professor (in Harry’s case, McGonagall) looks up children in the book every year:

In Hogwarts there's a magical quill which detects the birth of a magical child, and writes his or her name down in a large parchment book. Every year Professor McGonagall checks the book, and sends owls to the people who are turning 11.

— Online chat transcript, Scholastic.com, February 2000

Community
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alexwlchan
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    Since your answer is the more complete of the answers given so far, and more correct (with the details from Pottermore included), I hope OP decides to accept it (no offense to @DVK). – SQB Jun 30 '14 at 12:15