How does the yellow book influence Dorian?

The short answer is: not in a good way. The Yellow Book is given to Dorian by the decadent aristocrat Lord Henry Wotton. In the book, the protagonist becomes obsessed with experiencing as many aesthetic sensations as possible. In pursuit of this overriding goal, he pursues an immoral lifestyle, engaging in all kinds of depraved actions, no matter how evil, now matter how scandalous they're considered to be by respectable society. Love, friendship, integrity, none of that is remotely important to the louche protagonist of the Yellow Book; only sensations matter. The book's central message is that a life without repeated exposure to aesthetic sensation is not just boring but worthless.
When Dorian reads the book, he sees something of himself in the protagonist. Beauty is about the only thing he has going for him, so when he reads about a man who worships beauty like a god, he's completely mesmerized. Dorian's mind has been poisoned and seduced by the Yellow Book in equal measure, and from now on it will be his faithful guide as he sinks further and further into a foul, stinking mire of wickedness, degradation, and moral corruption.