It could develop slowly. At first, they might just be acquaintances who exchange polite greetings in the hallways. Then, they could be grouped together for a school project. Through working on it, they'd start to see each other's strengths and weaknesses, and a friendship would begin to form.
In fanfiction, if they met in high school, their relationship could be a case of 'opposites attract'. Percy, being more of an action - oriented person, would be intrigued by Annabeth's intellectual side. Annabeth, on the other hand, would be interested in Percy's courage. This mutual interest would lead to them spending more time together, like joining the school's Greek mythology club together. As they explore their shared interests further, their relationship would grow deeper, from friendship to a possible romantic relationship over time.
Their relationship might develop in a rather turbulent way. Since Percy is often impulsive and Annabeth is so headstrong, they could have a lot of arguments at the beginning. But as time goes by, they start to understand each other better. For instance, when Percy gets into trouble because of his ADHD - related impulsiveness, Annabeth could use her intelligence to help him out, and this would bring them closer.