Trivia: Initially, the last time Beetlejuice was to be seen in the film is when the sandworm devours him, giving the impression that he does, in fact, "die." However, test audiences found the character to be so likeable (despite being the villain) that they were unhappy with this being his ultimate fate, so an epilogue was added on where Beetlejuice is shown in the waiting room and gets his head shrunken.
Trivia: In one scene, Delia is wearing strangely baggy red pants held up with suspenders. This is actually a sweater that Charles was seen wearing earlier. It was flipped upside-down and repurposed into a pair of pants. This is one of a few instances in the film where Delia is repurposing clothing. Another example is in the first diner scene where the characters are eating Chinese food - in that scene, she's wearing a peculiar headband made of gloves.
Answer: They died by drowning. Jane's daughter even tells Lydia when she asks what happened. Although Adam and Barbara should have been completely wet for the whole movie, Tim Burton decided to keep Alec and Geena dry as he felt that keeping them wet the entire time would be an uncomfortable experience for both of them.