In the seventh book, Harry wonders if 'the trace' is still on him after his seventeenth birthday, as the Ministry of Magic/Death Eaters keep managing to track him, Hermione and Ron down. It is later revealed that Voldemort's name has been "tabooed", so that the location of anyone speaking it will be revealed, and the
However, in the first book, 'the trace' would only have worked if Harry was using magic- which, aside from setting a Boa Constrictor on Dudley, does not happen. The address(es) on the Hogwarts acceptance letter(s) sent to Harry are very specific:
"Mr H. Potter, The Cupboard under the Stairs, 4 Privet Drive, Little Whinging, Surrey"
"Mr H. Potter, The Smallest bedroom, 4 Privet Drive, Little Whinging, Surrey"
"Mr H. Potter, Room 17, Railview Hotel, Cokeworth"
At first I thought that the Anthony Horowitz book "Groosham Grange" (which was published a decade before Harry Potter and JK cited as an influential resource) might help provide an answer, as in the book a black crow is sent by the school to watch David. However, there are no mentions of Owls/other birds except for the ones delivering the (already addressed) mail.
It's possible that professor Trelawny used a crystal ball or her prophecy powers to watch Harry's movements, however, in 'The Prisoner of Azkaban', Dumbledore comments:
'Do you know, Harry, I think she might have been,' he said thoughtfully. 'Who'd have thought it? That brings her total of real predictions up to two. I should offer her a pay rise…' (PA22)"
As her first real prediction was the prophecy "neither shall live while the other survives", and the second was the one about "the servant returning to his master". Crystal-ball-gazing doesn't seem to extend to present events as such, and in any case, Dumbledore admitted in the quote that she wasn't a great seer, so what I'm wondering is:
How did the Hogwarts professors know (and in such great detail) where Harry was, and; Why couldn't this method be replicated in later books (such as when the Death Eaters wanted to track Harry)?
Additionally, does anyone have any idea how (Wizarding-world) Owls can manage to track people with no addresses written on them? E.g, in book 4, (aside from being a super-smart bird) how is it that Hedwig can easily find where Sirius is?