How did Percy, Annabeth, and Grover escape the underworld in The Lightning Thief?

Percy, Annabeth, and Grover use Percy's three pearls to escape from Hades and the underworld.

Percy, unfortunately, only has three pearls. If he uses them to save himself, Annabeth, and Grover, he won't have one left to save his mother. Both Annabeth and Grover try to persuade Percy to leave them behind so he can have a pearl for his mother. Percy refuses because he has decided he will come back and save his mother later.

Percy, Annabeth, and Grover break their pearls as the skeleton army is attacking them. The pearls turn into very strong bubbles that form a protective circle around each child. In these bubbles, the three children are carried back up to the earth, breaking the surface of Santa Monica Bay.

How do Percy and Grover return to NYC in Percy Jackson and the Olympians: The Lightning Thief?

Percy and Grover travel back to New York City by plane. As the deadline to return the Master Bolt to Zeus approaches, they do not have time for any other form of transportation.

Percy knows that flying is off-limits for him because Zeus, the god of Heaven, currently suspects him of being the "lightning thief"—the one who stole the bolt in the first place. Percy takes the risk, as he has no other choice, and hopes that having the bolt with him will serve as "insurance": if Zeus decides to "blast him out of the sky," he will destroy his own bolt. However, Percy is still anxious all throughout the flight, and his fears are not unfounded. When he finally returns the bolt, Zeus grumbles about Percy's audacity. Poseidon, the god of the ocean and Percy's father, intervenes and calms Zeus down, thus reassuring Percy that he has made the right choice.