We can find the answer to this question in Chapter Fourteen. Having murdered his friend, Basil Hallward, Dorian contacts one of his former acquaintances, Alan Campbell, who, like so many of his friends, was formerly always seen with Dorian Gray, until one day, "the intimacy had come suddenly to an end." We are told that this intelligent young man's passion was for science, and when he arrives, Dorian asks him to use his scientific knowledge to dispose of the body:
"What you have got to do is to destroy the thing that is upstairs--to destroy it so that not a vestige of it will be left... You, Alan, you must change him, and everything that belongs to him, into a handful of ashes that I may scatter in the air."
Of course, Dorian uses blackmail to persuade Alan to do this task for him. Though we never know what the nature of the information Dorian has about Alan is, it perhaps can be inferred that it is something to do with a sexual deviation or misdemeanour. Wilde himself was used to being blackmailed for his homosexuality.
Having committed the violent and shocking murder of Basil Hallward, his friend, in Chapter Thirteen, it is in Chapter Fourteen that we see how he determines to dispose of the corpse. Dorian summons another of his former friends, that, like so many others, now will no longer be seen with him at all, to his house. Once there, he asks Alan Campell to use his knowledge of science, and in particular chemistry, to make the body disappear completely. Note what Dorian says to Alan:
You know about chemistry, and things of that kind. You have made experiments. What you have got to do is to destroy the thing that is upstairs--to destroy it so that not a vestige of it will be left.
Of course Alan, rightfully so, wants nothing more to do with Dorian, so Dorian is forced to cold-heartedly blackmail his former friend into doing what he wants him to do by threatening to reveal certain unspecified information about Alan to the right people. We thus see more signs of Dorian's continued descent into the maelstrom of evil and moral corruption.