In The Amazing Spider-Man, Peter Parker becomes Spider-Man, fights Dr. Curt Connors as the Lizard and stops his plan to turn New York into lizard creatures. Spoilers follow.
Peter finds his father's briefcase and traces it to Oscorp and Dr. Curt Connors, a one-armed researcher who worked with his father. Inside the lab a genetically modified spider bites Peter, and he develops spider powers. He then gives Connors a piece of his father's research, which helps Connors move forward with his work on regrowing limbs.
Peter lets a thief get away, and that same man later kills Uncle Ben. Driven by that loss, Peter starts hunting criminals in a homemade mask and suit as Spider-Man. He grows close to Gwen, whose father, police captain George Stacy, wants the vigilante caught.
Under pressure from his Oscorp boss, Connors tests the formula on himself. He regrows his arm and turns into a violent reptilian creature called the Lizard. The Lizard attacks around New York, and Peter fights him several times.
Connors then plans to release a gas from Oscorp Tower that would turn the whole city into lizard creatures like him. Gwen and Peter work out an antidote, and Captain Stacy, who has learned who Spider-Man is, helps clear the way for him. Peter reaches the tower, battles the Lizard and spreads the antidote, which turns Connors back into a man.
Captain Stacy dies of his wounds and makes Peter promise to keep away from Gwen to protect her. Peter tries to keep that promise but tells Gwen he cannot stay away from her, and he returns to school and to life as Spider-Man.