‘How did I get the Stone out of the Mirror?’
‘Ah, now, I’m glad you asked me that. It was one of my more brilliant ideas, and between you and me, that’s saying something. You see, only one who wanted to find the Stone – find it, but not use it – would be able to get it, otherwise they’d just see themselves making gold or drinking Elixir of Life.’
Philosopher's Stone - page 217 - Bloomsbury - chapter seventeen, The Man With Two Faces - Harry talking with Dumbledore
Dumbledore doesn't directly answer Harry's question, but rather describes under what circumstances a person could collect the Philosopher's Stone from the mirror. Did Harry have to do anything to retrieve the stone, such as reach into the mirror and take it? If not, what kind of magic could have removed the stone from the mirror and put it into Harry's possession?
A canon-based answer is preferred, such as the books, interviews with J.K. Rowling, or info from Pottermore, but subjective answers within the spirit of canon are welcome.