Spoilers ahead for 13 Reasons Why Season 3. Though it's initially believed he was shot, that's not actually how Bryce died on 13 Reasons Why. In fact, we don't find out the real way he died until almost the end of Season 3, which leads Clay and Ani to wade through a lot of false leads before finding the truth.
When the season picks up, it's immediately clear that Bryce is dead — something you likely already knew if you watched any of the trailers. After the homecoming game between Liberty High and Bryce's new school, Hillcrest, devolved into an all-out brawl, he went missing, and he hasn't been seen for several days. Soon enough, his body is discovered in the river. And after finding prints and blood in his car, which was left at the pier nearby, his death is ruled a homicide.
At first, it seems like Bryce died of a gunshot wound, as there is a bullet-like wound in the back of his head. However, police later realize he was severely beaten, and thus attribute his cause of death to blunt force trauma. This is the assumption Clay and Ani operate with while trying to figure out who murdered Bryce, but that, too, turns out to be false: when Zach, believing he's the killer, goes to the police station to confess he beat up Bryce and left him on the pier, Deputy Standall (aka Alex's dad) reveals Bryce actually drowned. Medical examiners were able to determine that he was still alive when he ended up in the water.
Being that Bryce was such a complicated character, it makes sense that the circumstances of his death were just as complicated, and so was the process of figuring out exactly what happened the night of the homecoming game (which ended up being a mystery in and of itself).
As for who was responsible for Bryce's death, that's basically the point of Season 3, so fans will have to watch all the way to the final episode to find out for sure — including having to navigate all the twists and turns thrown in along the way. When the truth is revealed, it's by no means a clean ending. Yes, answers are provided, but as in previous seasons of 13 Reasons Why, those answers only beget more questions.
One thing that is clear? Bryce's death has a massive impact on the students at Liberty High. As news spreads that he was murdered, everyone immediately becomes paranoid that one of their friends could have been involved. It also brings up a lot of mixed emotions: there are a lot of people who are (understandably) happy Bryce is gone, but there are also people who were close to him at some point in his life and miss him in spite of all the pain and trauma he inflicted. The case may be closed for now, but the ramifications of Bryce's murder will undoubtedly spill into the show's fourth and final season.