I heard about these dragons on this site and was curious to know, when do legendary dragons appear in the world? Is there a step-by-step guide to getting them to appear?
Legendary variants of dragons were added for high-level players; they begin to appear at around level 78. Once you get that high, they can be found just like any regular dragon (although they are not guaranteed to spawn): randomly in the wilderness, at word walls, et cetera.
Note that Legendary dragons were added by the Dawnguard DLC, so you'll need that.
There is a guaranteed spawn at Arcwind Point.
A legendary dragon can also always be found at Arcwind Point perching above a sarcophagus that contains either a Draugr Deathlord or a Dragon Priest.
This spawning point still requires the The Elder Scrolls V: Dawnguard DLC and level 78+. If the player dose not meet these requirements, another type of dragon will spawn at Arcwind Point.