There are various ways. It could be related to a special prophecy. For example, if there's a prophecy that talks about a new god rising from the ashes of a great battle. You might be a mortal caught in that battle, and due to your actions during it, you get reincarnated as a god. Another way could be through a deal with an existing god. If you manage to strike a bargain with a god who has the power to transform you, you could end up as a god in the Percy Jackson fanfiction world.
In most Percy Jackson fanfiction, it often involves some sort of magical or mythical event. Maybe you die heroically in the mortal world and are then chosen by the Fates to be reincarnated as a god. Or it could be through a powerful magic spell that goes awry and instead of something else, turns you into a god.
Often in Percy Jackson fanfiction, becoming reincarnated as a god might be tied to a unique item or location. There could be a magical spring that, if drunk from, can transform you into a god under the right circumstances. Or it could be an ancient artifact that, when activated by the right person (you), causes you to be reincarnated as a god. It also depends on how the author of the fanfiction wants to set up the rules for this transformation, as there's a lot of creative freedom in fanfiction.
The best chapter pointer here is Chapter 31, "Master, I've been having some bad luck lately!". It opens with Before Shen Lan had reached the backyard, she already heard the sounds of... and closes on After staying in the study and reading for another day, she finally....
A practical answer is Chapter 52, because it turns the idea into a concrete scene. The chapter opens with The village chief and the woman behind him exchanged a glance, "This..., adds pressure through A grown man, dressed so flamboyantly, looks utterly terrible, couldn't..., and ends on And at.
Chapter 44 is the strongest chapter-level answer because it starts from But the next move by the production team proved they hadn't forgotten the... and follows through on Does anyone here know how to drive?.
If you want the clearest chapter reference, go to Chapter 33. Early on, Following the announcement, five artists respectively reposted the Weibo—...; later, the chapter leans on Instantly, "Shining Transformation Trip," already under intense scrutiny,....
A practical answer is Chapter 50, because it turns the idea into a concrete scene. The chapter opens with [666, if good scores determine rankings, is Flash Change's production team..., adds pressure through I wouldn't wear such ugly shoes!, and ends on What kind of heavenly being had such a sour.
Look to Chapter 73 for the clearest answer. It begins with Director Sun, tongue-tied, finally managed to squeeze out a sentence,..., keeps building through But isn't it due to your production team's lack of consideration?, and lands on Despite Wen Jiaojiao's fiery temper, there were still many who.
The best chapter pointer here is Chapter 53, "Save People!". It opens with Night had fallen over Chixia Village, eerily void of any human sounds. and closes on Wait, did this kid accidentally fall into the water?] [Help, this camera....
If you want the clearest chapter reference, go to Chapter 72. Early on, Jiang Yan was still griping when suddenly a fair hand reached out beside...; later, the chapter leans on I'll take these, thank you." In an instant, five pairs of eyes stared over....
Chapter 51 is the strongest chapter-level answer because it starts from Oh, okay." After uttering two syllables indifferently, Jiang Li bent down... and follows through on If I opened a bar here, wouldn't I become a savior?" Jiang Yan was....
The best chapter pointer here is Chapter 71, "The Theme of the First Day—Breaking New Ground!". It opens with Shu Yan curled her lips with a hint of jealousy, "When can it be my turn... and closes on Now they had to work on an empty stomach..