My boy started reading on his own when he was four. It started out with the usual: him picking out certain words at story time. And then I guess he must have been scanning the words as we read to him. Later, he said that I had taught him. Not true, but maybe he was sitting in my lap and looking on as I read when the breakthrough happened for him. My brilliant wife read to him half the time, as we alternated putting the kids to bed. Now she does it by herself every night.
Then the little guy would grab a kid book and sit on the couch looking at it for extended periods. He did this longer and longer with more and more books, then started telling us what was in the books. "He's reading!" I said to my kind wife, but I think she did not want to admit that then. So I tested him by printing out sentences I had written on the computer.
I'd say he was four and a half by the time we all accepted that he could read.
Now his equally smart sister is three and a half. So he tells her and us too that he started reading when he was three and a half.
Saturday morning they were playing word bingo and she found some words like "fun," "run," "we" and "go" on her own. "Now you know how to read!" he said generously.