Annabeth and Grover prove their loyalty and friendship to Percy in The Lightning Thief by following and helping him through the many dangers that crop up during Percy's quest. Moreover, Annabeth and Grover both plainly tell Percy that his friendship matters to them. While riding in the 'Kindness International' truck, Annabeth lets Percy know that she would willingly take his side if the gods divided into a war:
"'I don't know what my mom will do. I just know I'll fight next to you.'
'Because you're my friend, Seaweed Brain. Any more stupid questions?'" (251).
Both Annabeth and Grover prove resourceful companions, whether they are fighting Medusa or trying to escape from Hephaestus' booby-trapped Love Boat ride. Even when the quest becomes seriously dangerous and part of Percy's plan means venturing into the Underworld, Grover and Annabeth show their loyalty to Percy by backing him up every step of the way.
They help Percy with the difficulties he faces, such as when he encounters Medusa.