What advice does Lord Henry give to Dorian?
Lord Henry's advice is, essentially, to live life to the fullest while he is young, before the ravages of time sap him of his youth. He should, Lord Henry tells him, live for himself, and for no other:
...realize your youth while you have it. Don't squander the gold of your days, listening to the tedious, trying to improve the hopeless failure, or giving away your life to the ignorant, the common, and the vulgar. These are the sickly aims, the false ideals, of our age. Live! Live the wonderful life that is in you! Let nothing be lost upon you.
Henry says that the world needs a "new hedonism" in the form of people like Dorian, who should only be guided by the search for beauty and especially pleasure in life. Just after this speech, Basil finishes his portrait of Dorian, and the young man is struck by the youthful likeness, and by the knowledge that, as Henry has just warned him, that his beauty will be fleeting. It is at this point that Dorian says that he wishes that the picture would grow old instead of him:
If it were I who was to be always young, and the picture that was to grow old! For that—for that—I would give everything! Yes, there is nothing in the whole world I would not give! I would give my soul for that!
Of course, this is more or less what ends up happening, with destructive results. The painting, a likeness of the real Dorian Gray, becomes hideous, a reflection of his soul as he lives the lifestyle of debauchery and hedonism recommended to him by Lord Henry. In any case, Dorian reveals that he has found Lord Henry's speech profoundly convincing, and exclaims that one's youth and beauty is really the only thing "worth having."