What is the legend about moon-letters?

As for the first part of your question, “Moon-letters are rune-letters, but you cannot see them,” said Elrond, “not when you look straight at them. They can only be seen when the moon shines behind them, and what is more, with the more cunning sort it must be a moon of the same shape and season as the day when they were written. The dwarves invented them and wrote them with silver pens, as your friends could tell you. These must have been written on a midsummer's eve in a crescent moon, a long while ago.”

What they revealed;

“Stand by the grey stone when the thrush knocks,” read Elrond, “and the setting sun with the last light of Durin's Day will shine upon the key-hole.”