Question: How did Palpatine come back? Cloned? Or somehow survived the Death Star explosion, which seems unlikely.
Answer: It is not said exactly how he came back. He says that he had died before which presumably is him dying in ROTJ. The most we get is the reference to Sith ability that some consider unnatural.
It is not said how he came back, but I get the idea that he was using the Force to keep himself alive. At least that's the message I was getting when I saw that Palpatine's fingers were wilted away. And I thought that the power he was using was urging his life to go on, but his physical appearence was being dragged behind.
Answer: The line "The dark side is a pathway to many abilities some consider to be unnatural" is a direct reference to Star Wars Episode III: Revenge of the Sith, in which Palpatine says the same line verbatim to Anakin. Recall that a major plot point to that prequel is that the Sith have long been rumored to have found a method to cheat death. This film strongly suggests that Palpatine had indeed discovered this method. The film doesn't go into specifics. My understanding is the novelization says his body is a clone. Going by his appearance in the film (blank eyes; body manipulated by machine), it suggests to me that he is a reanimated corpse.
Chosen answer: According to the novelization, Palpatine sensed Vader's internal conflict and created a clone as a backup in the event that Vader betrayed him. When Vader threw him down the shaft, Palpatine transferred his consciousness into the clone's body.