The full story
Reed Richards and Sue Storm are trying to get married, and thinking about leaving the Fantastic Four for a normal life, when something starts tearing craters across the planet and knocking out power. It reaches New York during the wedding. Johnny chases it, finds a silver alien on a flying surfboard, and is easily beaten. The encounter leaves Johnny swapping powers with any of the others he touches.
Reed traces the Surfer back through the planets he visited before, all of them destroyed, and works out that London is next; the Four can't stop him from draining the Thames. Passing over Latveria, the Surfer frees Victor von Doom from his frozen state. Doom confronts him and loses, but the clash restores his human body, and he uses what he learned to get the US military to force the Four to work with him.
Reed separates the Surfer from his board, the source of his power, and the military imprisons and tortures him. Sue gets in to see him and learns the truth: he serves Galactus, a vast cosmic entity that consumes living planets, and his service is the price of his own world's survival. The board is the beacon leading Galactus here. Doom steals it for himself. The Four free the Surfer and chase Doom to Shanghai, where he impales Sue. Johnny takes all four of the team's powers at once and, with Ben's help, beats Doom and gets the board back.
Inspired by Sue, the Surfer brings her back to life, then flies up to meet Galactus as he arrives, and a huge blast of energy engulfs them both. Earth is saved, and Johnny can no longer swap powers. Reed and Sue are married in Japan. In a mid-credits scene, the Surfer drifts through space, apparently lifeless, until his eyes open and his board flies back to him.