It's a dark and stormy night. A casket sits in an enormous room in a castle. The lid is opened to reveal a corpse clutching an ornate metal box. Someone takes the box, but the skeletal corpse doesn't let it go without a fight.
This is our first hint that we might be in a Mel Brooks movie.
Meanwhile, Dr. Frederick Frankenstein (pronounced "Fronkensteen" by his own insistence), a professor of neurosurgery at an American university, is teaching a class about the human brain. While explaining the difference between voluntary and involuntary nerve impulses, he's interrupted by a brainiac student pestering him about his infamous grandfather's work in "the reanimation of dead tissue." (i.e. bringing corpses back to life, not trying to revive Pushing Daisies for a third season.)
Frederick explodes, yelling that his grandfather was a "cuckoo" and he wants no part of that lunatic and unscientific work. After class, an old man holding the aforementioned metal box approaches him. His great-grandfather's will has been read, and Frederick's been left a big ol' creepy castle in Transylvania. Instead of selling it (the Transylvanian housing bubble went bust after that vampire incident), he takes a train to Transylvania to check it out.
At the castle, he meets Igor and Inga. One is hunch-backed and bug-eyed, the other is a beautiful buxom blonde. Guess which is which. The caretaker of the castle, Frau Blucher, shows Frederick to his room, which once belonged to his grandfather Victor. After a restless night tormented by dreams about his inescapable destiny, Frederick's awakened by creepy violin music, and he and Inga find a secret passageway behind ze bookcase, which is German for "the bookcase."
Ze passageway leads to ze laboratory; the exact same laboratory where Victor Frankenstein once reanimated a corpse. Frederick finds gramps's library and his book, titled How I Did It, which details how he did it. "It" being bringing the dead back to life.
Obsessed, Frederick digs up the corpse of a criminal who's just been hanged, and intends to replace the brain with that of Hans Delbruck, "scientist and saint." Igor drops the jar with Delbruck's brain and instead grabs a brain from another jar in the lab. He doesn't notice the warning sign of "Abnormal" in front of this particular brain. Frederick performs the brain transplant and waits.
The monster wakes up and tries to strangle the Doctor, but Inga sedates the monster. At that moment, Inspector Kemp shows up to check things out. The villagers are restless, worried that another Frankenstein has taken up residence at the castle. Frederick pretends to be normal and Kemp leaves satisfied, avoiding another angry mob. However, Frau Blucher, who was in love with Victor, lets the monster go. The monster stomps around the village a bit before Frederick lures him back by playing the violin's tune.
In a hopeless public relations effort, Frederick teaches the monster to walk and talk (kind of) and the two put on a very scientific production. They sing "Puttin' on the Ritz" or, as the monster says it "putthtanttaonaraarttizah," and dance in top hat and tails. A light bulb on stage bursts, and the monster, being scared of fire, goes wild and is restrained by the police.
Back at the castle, Frederick's fiancée Elizabeth arrives via carriage just as Frederick and Inga have finished having a little roll in ze hay in the laboratory. The monster breaks free of his chains and kidnaps Elizabeth, carrying her to a barn and impressing her with his giant schwanstucker. Elizabeth finally finds what she's been looking for.
The doctor lures the monster back to the castle with the violin again and attaches him to a machine to perform a "transference." He intends put part of his mind into the monster. The procedure is almost complete when the villagers arrive with torches and pitchforks. They tear the doctor from the machine, but all of a sudden, the monster shouts, "Put that man down!" When the monster talks, everyone listens. But the doctor remains motionless. Fade to black…
When we return, the monster and Elizabeth are married and are living in domestic bliss, or a reasonable facsimile of bliss. The doctor survived and married Inga, making her Mrs. Frankenstein, and they even pronounce the name correctly now. When Inga asks the doctor what he got from the monster in the transference procedure, he shows her off-screen… seems like he got a little bit of the monster's schwanstucker in exchange.