In the beginning of Goblet of Fire, Harry sends Snuffles a letter. Hedwig somehow finds him after the extremely specific command from Harry, "Just find him, okay?"
Theories:
Now I know that owls are intelligent beings in the Harry Potter canon. But.... those ideas are just as crazy as the next.
So how did Hedwig do it?
From JK Rowling's own writing on Pottermore:
"Whether because they possess an innate bent for magic (just as pigs are reputed to be innately non-magical), or because generations of their ancestors have been domesticated and trained by wizards and they have inherited the traits that make this easy, owls learn very quickly, and seem to thrive on their task of tracing and tracking the witch or wizard for whom their letters are intended.
The mystical association between the name and the human who bears it has long been understood by witches and wizards of all cultures. While the process remains mysterious even to those who train up owlets to become wizarding pets or postal owls, the birds appear to be able to make such a connection between the name and its possessor that enables them to trace the witch or wizard concerned wherever he or she may be. An owl does not need to know an address, although witches and wizards generally add the place to the envelope on the off-chance that the owl is intercepted and the letter falls into other hands."
So it's a mostly mysterious branch of magic at least to most - Kind of like wand lore or the subjects of the Department of Mysteries, but most owls can do it.
