Lateral Thinking Puzzles, unlike most puzzles, are inexact. In a sense, they are a hybrid between puzzles and storytelling. In each puzzle, some clues to a scenario are given, but the clues don't tell the full story. Your job is to fill in the details and complete the story. Obviously, there is usually more than one answer to any given puzzle, but, in general, only one solution is truly satisfying.
You can try solving these puzzles on your own -- that's certainly a legitimate way to go about this -- but usually you can have more fun if you involve other people. The way this works is, you look at the answer (maybe you want to try the puzzle on your own first!), then read just the clues to your friends. Your friends must determine the answer by asking questions about it, which you may answer only with yes, no, or doesn't matter. You can adjust the difficulty of the puzzle by varying the initial clues, throwing in red herrings, and so forth.
Warning: For some reason, these puzzles have a tendency to be rather morbid.