"What exactly did that entail?"
This is from wikipedia, FWIW:
The moments of shooting were recorded in cellphone footage from multiple angles. Around 11:45 pm, video footage showed Rittenhouse being pursued across a parking lot. As an unknown person fired a shot nearby, Rosenbaum chased after Rittenhouse, throwing something in his direction, identified in some reports as a plastic bag. According to Kenosha County prosecutors, Rosenbaum tried to take Rittenhouse's rifle from him. Rittenhouse then fired four shots, hitting Rosenbaum in the groin, back, and left hand. The bullets fractured Rosenbaum's pelvis and perforated his right lung and liver. Rosenbaum had additional minor wounds to his left thigh and forehead. Rittenhouse remained near Rosenbaum and made a phone call as a bystander began administering first aid to Rosenbaum. Rittenhouse was heard saying into his cell phone, "I just killed somebody." He then fled.
In another video, Rittenhouse was filmed as he continued to be chased down the street by several other protesters before tripping. According to the criminal complaint, at that point, protesters are heard yelling, "Beat him up!", "Get him! Get that dude!", and "Get his ass". After he fell, one of the men who had been chasing Rittenhouse began to kick and attempt to disarm him, with Rittenhouse firing two shots, missing this man. Another protester, Anthony Huber, next struck Rittenhouse with a skateboard. According to court records and video footage, Huber struck Rittenhouse's shoulder or head/neck area with his skateboard, and tried to grab the rifle. Rittenhouse shot Huber once in the chest, perforating his heart and right lung. Gaige Grosskreutz also approached Rittenhouse; when Huber was shot, Grosskreutz stopped and put his hands up. When Grosskreutz moved again towards Rittenhouse, Rittenhouse shot Grosskreutz in the arm. According to court records, Grosskreutz appeared to be holding a gun. Grosskreutz has acknowledged that he was carrying a gun. Gunshots from other sources can be heard around the same time of Rittenhouse firing his shots from the ground.
Rittenhouse subsequently walked towards police with his hands up and the semi-automatic rifle strapped across his chest; they allowed him to leave or appeared not to acknowledge Rittenhouse, though several witnesses and other protesters shouted for him to be arrested. When asked at a press conference why Rittenhouse was not stopped, Kenosha Sheriff David Beth said, "In situations that are high-stress, you have such incredible tunnel vision" and implied officers may not have realized he had been involved in the shooting. Likewise, Kenosha Police Chief Daniel Miskinis claimed that "there was nothing to suggest this individual was involved in any criminal behavior" due to the fact that someone walking towards the police with their hands up was "no longer abnormal" in the wake of the protests.