In answering this question, you should look to find examples of Gothic motifs in the text. Examples of Gothic motifs include a scary or frightening atmosphere and references to the supernatural. By looking for evidence of these motifs, you will find the most significant examples of Gothic style in the novel.(You can find more examples of Gothic motifs in the reference link provided below.)
Beginning with the first example, let's consider the creation of a scary atmosphere in The Picture of Dorian Gray. This is, perhaps, best shown in the opening of Chapter 16, when Dorian heads to the opium den:
"A cold rain began to fall, and the blurred street-lamps looked ghastly in the dripping mist. The public-houses were just closing...From some of the bars came the sound of horrible laughter. In others, drunkards brawled and screamed."
In creating this tense atmosphere, Wilde hints at the events which follow, specifically the attempted murder of Dorian Gray by James Vane.
Next, consider using a strong example from the text of the supernatural. Arguably, this comes first in Chapter 2 when Dorian sees his completed portrait for the first time. He is so overwhelmed by his own beauty that he says: "If it were I who was to be always young, and the picture that was to grow old!" This is followed by Dorian's assertion that he would sell his soul to the devil to make it so.
We do not realise the supernatural implication of this until Chapter 7 when Dorian notices that the portrait has changed: "The expression looked different. One would have said that there was a touch of cruelty in the mouth. It was certainly strange."
This supernatural element, so characteristic of the Gothic style, now sets the scene for Dorian's fall from grace and, ultimately, his own suicide.