Being dead doesn't keep him from communicating with Harry through his portrait or through an as yet undiscovered horcrux or two-way mirror.
By the way, the image in the portrait wouldn't be Dumbledore. It's an image of Dumbledore, with his memories and thought patterns, etc. But if Dumbledore went to whatever great beyond there is beyond this realm, that guy isn't the one in the paintings.
As for horcruxes, I'd find it hard to imagine that Dumbledore would create one. And Dumbledore probably expected to die, which would explain putting so many thoughts into his pensieve and telling Harry about them. He can guide him that way as well.