The differences are HUGE.
In the original novel, the Monster was designed to be beautiful and was alert, fast, strong, and downright eloquent in his speech. Upon animating, his beauty became a sick mockery of what the Doctor had intended, and the Monster was described as 'hideous'. This, and his strength, are all that remains of the monster from the novel, when transferred to the movie.
The original novel is bookended with narration by a seaman in the arctic, Captain Walton. The ship has picked up a man who was on the ice, on a dogsled, nearly frozen. This man is Victor Frankenstein. The rest of the novel recounts Frankenstein's story, as told to the Captain.
The book had no hunchbacked assistant, and no abnormal brain. The Monster turned out just as Frankenstein intended...Science went Horribly Right (TV Tropes).
In the book, the Doctor betrayed his creation first by abandoning it immediately after granting it life, then by destroying a second monster, designed to be its bride. The Monster had intended to take his bride to distant lands, where none but they could live, and live with her in peace. The Doctor, just before giving the Bride life, chose instead to destroy it, tearing it asunder, so as to not create another abomination (as he supposed the Monster to be).
The novel also featured the Monster killing (or being responsible for the deaths of) most of the Frankenstein family: Victor's brother, wife, and best friend. Victor's father dies of illness after this. Thus, in the books, the Monster and Victor are mutually antagonistic, with the book culminating in Victor swearing to follow the Monster to the ends of the Earth, until one of them destroys the other.
Victor dies. The Monster realizes that the death of its creator brings it no peace, and vows to the Captain that it will build a funeral pyre, and immolate itself.
In short, the movie took the core elements of the novel - a man playing God, and the awful ramifications, and put them into a frame that could be easily shot. It based its work off of a play which had already done much of this: the play required a manageable number of sets, a small number of characters, etc. All of these made the play a good source for the movie, but they lost most of the specifics in the transition.
The only real similarities between the novel and the original movie are character names, the moral, and the fact that the Monster kills people.
Wikipedia includes a bit more information.