In some fanfictions, it might be that he stumbles upon an old, enchanted object that gives him this power. He could be exploring an abandoned part of the castle and find a strange amulet. As soon as he touches it, he feels a connection to the elements and realizes he can manipulate the weather. It starts with small things like making a light rain stop.
Well, perhaps he first notices it during a really intense storm at Hogwarts. Maybe he's out in the courtyard and suddenly the wind starts to change direction as he gets a strange feeling inside. It could be that he was in a Quidditch match and the clouds above started to move in an odd way when he was concentrating hard on winning.