Continuity mistake: When Maya is arrested, she starts manifesting her powers on the policeman. In a close-up, we can see the black ooze coming out of her eyes. Cut to a shot from above, when the policeman's eyes turn black and he drops the handcuffs, and Maya's cheeks are suddenly clean again, with no trace of the black stuff. (00:33:45)
Factual error: When Nathan goes to Cork to find his brother, he gets out of a black cab with a yellow license plate, both of which are characteristic of ENGLISH taxis, not Irish ones.
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 ★