How to prove beyond a reasonable doubt?

Could you elaborate on the concept of proving something beyond a reasonable doubt in the context of legal proceedings? What specific steps are typically taken to ensure that the evidence presented is sufficient to convince a jury or judge of the defendant's guilt? How does this standard of proof differ from the lesser standards of 'preponderance of the evidence' or 'clear and convincing evidence'? And what are some challenges that prosecutors and defense attorneys may face in trying to meet or rebut this standard?