As mentioned already, Victor does use the body parts of the dead in creating his monster, however, he also uses pieces of dead animals. The line about "the dissecting room and the slaughterhouse" (Frankenstein chapter 4) reveals that not only has Victor stolen bodies from mortuaries and graves, but also used animal body parts to complete his creature. While Victor originally tries to create life just out of human parts, it seems he runs out of un-corrupted bodies and has to resort to the animal dead. While Shelley is not overly graphic about the process itself, the connotations are still quite terrifying. The closest thing to a description of the creature she gives is in chapter 5 when the creature is brought to life: 

"His yellow skin scarcely covered the work of muscles and arteries beneath; his hair was of a lustrous black, and flowing; his teeth of a pearly whiteness; but these luxuriances only formed a more horrid contrast with his watery eyes, that seemed almost of the same colour as the dun white sockets in which they were set, his shrivelled complexion, and straight black lips.”

Although the creation of the monster is fairly tame, it suggests such horror and his creature is so grotesque that it's more than enough to shock the reader. According to the story, when Mary Shelley was first telling her story and got to the section of the story when the creature comes to life, her husband, Percy Shelley, ran from the room screaming. If that's not effective storytelling, then nothing is!