Emiya Shirō, mysteriously reincarnated into the world of Bleach, finds himself entangled with the Shihōin clan, especially Yoruichi, with whom he shares a complicated (and honestly, pretty toxic) relationship.
He starts off without a Zanpakutō, but his strange abilities and sharp combat instincts quickly draw attention. Before he knows it, he's engaged to Soifon, not by choice, which only adds another layer of chaos to his already stressful life.
Under Yoruichi's intense (read: borderline sadistic) training, and Soifon's unreasonable behavior, Shirō struggles to stay sane. He also has run-ins with familiar faces like Unohana, Shunsui, a young Byakuya, and Urahara.
Still, after countless ridiculous training sessions, Shirō gradually starts to grow stronger. Eventually, the story shifts as he parts ways with Yoruichi (not permanently) and heads off to enroll in the Shin'ō Spiritual Arts Academy to begin the next chapter of his journey.
TL:
Yeah, Shirō is kind of pathetic early on, and a lot of the first chapters are just him being trained (and bullied) by Yoruichi. If that's not your thing, feel free to skip ahead to Chapter 32.