The rule
What it is
In Hearts you try to take as few points as you can. Shooting the moon turns that around: take all of them. A player who takes every heart and the queen of spades in one hand, all 26 points, scores nothing for it, and each of the other three scores 26.
An example
In a game to 50, Ana, Ben, Cleo and Dev have 18, 22, 31 and 9 points. In the next hand Ben takes all thirteen hearts and the queen of spades. Ben scores nothing, and Ana, Cleo and Dev score 26 each.
That makes 44, 22, 57 and 35. Cleo has passed 50, so the game ends, and Ben, who was third, wins it.
Playing for it
Why it's a gamble
A shot at the moon has to take every point. If one heart goes to somebody else, the shot fails, and the player who tried keeps everything else they took: as much as 25 points in one hand.
When to try it
Look for a hand that can win tricks and keep winning them: high hearts; the queen of spades, or the ace and king of spades to catch her with; and long suits headed by their top cards. Low cards are the danger, because each one can hand the lead to somebody who won't give it back.
It helps to start quietly. Take tricks the way anyone might, and show your hand only when it's too late to stop you.
How to stop it
If one player has taken every point so far, it may be a run at the moon. Stopping it takes only one heart: win a trick with a heart in it, or keep a heart high enough to win one late in the hand. A few points on your own score cost far less than 26.
So don't throw your highest heart away just because hearts are bad: late in the hand, it may be the only card that can stop the moon.
Here and elsewhere
At Open Hearts
When someone shoots the moon, the table shakes around them, and the score sheet says who did it. Your profile counts, for your games alone, the moons you've shot and the ones you've blocked: hands in which somebody else took the queen and ten hearts or more, and you took one of the rest.
Other ways to score it
Some tables let the shooter take 26 off their own score instead, which matters when adding 26 to everyone else would end the game with the shooter still behind. Some count taking all thirteen tricks, “shooting the sun”, as worth more. Here the moon is always scored the same way: nothing for the shooter, and 26 for everyone else.