How is Percy Jackson related to the hero's journey ?

The Hero's Journey is an archetypal path that describes the narrative arc of many stories. It applies equally to ancient myths such as Homer's Odyssey and to modern stories like Star Wars. It begins with the hero living in the ordinary world, and ends with the hero's triumphant return bearing an artifact of power. 
Drawing a total parallel between the events of all five Percy Jackson books and the entirety of the twelve-part Hero's Journey is beyond the scope of what I can answer in this context. However, I can get you started on a few of those points:

The ordinary world: Percy lives with his ordinary step-father and his 'ordinary' mother, attending an ordinary high school and thinking he's an ordinary kid.

The call to adventure: Mrs. Dodds reveals herself to be a monster, attacking Percy

Refusal of the call: Percy explains his history of strange occurrences and 'hallucinations,' and the stress and doubt this experience has called him.

Meeting with the mentor: Chiron discards his disguise as Mr. Brunner and introduces himself properly to Percy.
There are eight more steps in the journey after this one. Depending on your interpretation, you can argue that they all occur over the course of the Lightning Thief, or you can view them as taking place across all five books of the Olympians series. Either way, follow the citation below for a breakdown of the entire journey, and consider where the various steps occur as you keep reading. Good luck!