Once Upon A Time In Texas - S4-E8
Continuity mistake: While talking to Claire outside the diner, Noah comments that he's looking forward to seeing her at the Homecoming game. But in season 1, Noah knew Sylar was going to try and kill Claire at Homecoming and had forbidden her from going.
Chosen answer: It's not been made 100% clear. It was originally assumed that he actually consumed part of the brain, but this has turned out not to be the case. Sylar has been shown all along to have an instinctive knowledge of how things work and how to fix them - this is his actual original power and the ability that made him an exceptional watchmaker and repairer. It appears that he uses a similar process when acquiring new powers - he exposes the brain of the target, allowing him to examine it and determine how their power functions. He can then apply that knowledge to his own brain, allowing him to replicate the ability in question.
Tailkinker ★