Seven Minutes to Midnight - S1-E8
Continuity mistake: When Mohinder is back in India, his mother tells him that his sister Shanti died at the age of 5, when Mohinder himself was 2. In "The Hard Part", Mohinder tells Molly Walker that Shanti died before he was born, and shows her a photo of Shanti (who looks 5 years old) and his pregnant mother.
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 ★