The most obvious instance of the first of these is Dorian's wish that he will never age and that the portrait will age instead—of course, this is what ends up happening, except for...
I would single out three devices Wilde uses with particular skill: foreshadowing, irony, and symbolism.
The most obvious instance of the first of these is Dorian's wish that he will never age and that the portrait will age instead—of course, this is what ends up happening, except for one thing. In addition to "aging," the portrait also reveals Dorian's soul, his inner self and the "evil" he has become. This in itself leads to the second literary device, irony. It's ironic that Dorian, in making this wish, thinks the outcome will be something good for him. It turns out that the alteration of the portrait becomes a kind of self-perpetuating process. When Dorian notices that the picture has changed, after his first reprehensible act in rejecting Sibyl, this somehow causes him fatalistically to accept his descent and willfully to continue his downward spiral. And the portrait becomes more and more loathsome as he does so.
A second instance of irony, probably not often noted, is that Lord Henry, although a cynical man and a bad influence ultimately upon Dorian, is also a man who casually accepts the imperfections of the world, is amused by them, and even revels in them. Ironically it's precisely the opposite quality—perfectionism—that causes Dorian to blast Sibyl after her bad performance in Romeo and Juliet and then to cast her aside. It's doubly ironic that Dorian's desire for perfection in the world marks the start of the downward spiral of his life.
Another ironic element is that although we are never told precisely what Dorian is doing that makes him so "corrupt"—until the murder of Basil, at any rate—this corruption is the centerpiece of the story. The reader can assume many things, though the obvious ones mostly have to do with sex, both straight and gay. We are told that Dorian has caused women to be disgraced and also that he has a "fatal effect on young men." He and Alan Campbell had been the best of friends, absolutely inseparable. But then, we are told, something bad happened between them. When Dorian calls Campbell to the house to dispose of Basil's corpse, Campbell's attitude to him, even before being told about the grisly task, is hostile in a shameful, unforgiving way. Of course, in nineteenth-century English and American novels (unlike, for instance, French and Russian works of the same period), we are typically never given direct information about intimacy even between married men and women. So Wilde is not unusual in that respect, but the unique thing about The Picture of Dorian Gray is that something sexual forms the heart of the book, and it's therefore ironic that the reader must guess as to what exactly is happening. A less important point, incidental in itself, is that in his state of "corruption," we are told that Dorian "had a special passion, also, for ecclesiastical vestments, as indeed he had for everything connected with the service of the Church." It's possible that in the irony of this, Wilde is making an underhanded comment against religion, saying that the trappings of religion are attractive to "evil" people.
Wilde's use of symbolism can be seen in the choice of names for some of his characters. Sibyl Vane is not actually vain, but this is the way men view her, including her own brother James. When she appears on stage she's described in typically sexist language, as if she were a beautiful porcelain doll of some kind. The men, including Dorian, interpret her as being obsessed with her own looks to the exclusion of all else, though this is obviously not true.
Dorian's own name, Gray, is symbolic of an ambiguous middle ground between light and dark. He represents perfection and youthful innocence at first, and then corruption and evil later. As the story progresses, the dichotomy within Dorian—between his innocent appearance and his true self shown in the portrait—becomes worse and worse and is never resolved, for the two halves of Dorian are not brought back together but are in effect merely switched at the conclusion. The ugly portrait becomes the dead man, and the youthful, uncorrupted-looking man becomes the portrait again. This is the final irony, that in attempting to destroy the picture, Dorian destroys himself.