I know how to cause a checkmate in three moves. Are there any better ones? I've been told that there is a two move one but, I have never found someone who can do it. Is it just a legend that has happened once or twice?
There is a two-move mate: the Fool's Mate. However, it requires White to be, as the name implies, extremely foolish!
[FEN ""]
1.g4 e5 2.f3 Qh4#
As you can see, this mate relies on White advancing pawns without any regard for his King's safety. There's no way to force a two move checkmate (if there were, Chess would be an awfully boring game!).
As to whether it's ever occurred in real (master) play, I can't find any record of it, though the Wikipedia article mentions Teed vs. Delmar, 1896, where a very similar mate is delivered a few moves later.
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4I remember teaching someone to play and the first game we played was exactly this series of four moves. It was surreal. – Kyle Jones Aug 6 '14 at 1:25
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In her final round Gibralter Masters game, Hou Yifan attempted something like this as white, however black did not play 1. e5. Read about that infamous game/story for instance here: chessbase.in/news/gibhou – user1583209 Nov 13 '19 at 15:13
You can NOT cause a mate in 3 or 2 or any low number.
If the other player is truly stupid or messing with you then it might be possible to mate in 2 for black but white to do it would take 2½