We learn in Ch. 7 (VII) that William has been murdered, although we do not yet know why. All we know is that he was found dead after wandering off and it appears he may have been choked or strangled because there was "the print of the murderer's fingers on his neck."
It is not until Ch.16 (XVI) that we know why William was murdered and by who. At this point, the novel is being narrated by the Creature and he tells us he was walking through the countryside one day, dwelling on his unbearable loneliness. He sees a little boy not too far off and the idea crosses his mind that this little boy is too young to have any real "prejudices" and if he were to capture and educate the boy, then he would be able to cultivate a real friend. So, he literally goes up to the little boy, William, and grabs him. This scares William, obviously, and he screams. He also tells the creature to let him down because his will tell his papa, and then he says that his father is M. Frankenstein (Victor's father). This enrages the Creature and he responds with:
"Frankenstein! You belong to my enemy—to him towards whom I have sworn eternal revenge; you shall be my first victim."
William struggles more, and in the process he calls the Creature a bunch of names, which makes the Creature even more upset, so the Creature clasps William's throat with his hand to "silence him," and ends up actually killing him. The Creature is happy about this, as he now realizes he, too, can cause destruction.