To clean a burnt saucepan effectively, common and proven methods include using baking soda, vinegar, lemon, or a combination of these ingredients with heat and scrubbing:

• Remove loose burnt food and debris first.
• Heat the pan with water or a water-vinegar mix to simmer and loosen burnt bits ("deglazing technique").
• Add baking soda to the cooled pan bottom and scrub with a wet scouring pad or nylon brush.
• For tougher burnt residue, boil vinegar in the pan, then add baking soda to create a fizzing reaction that loosens grime before scrubbing.
• Alternatively, sprinkle baking soda and scrub with a lemon half for a natural mild acidic abrasion.
• Using crumpled aluminum foil with baking soda paste is an effective abrasive scrub for metal pans.
• Dishwasher tablets can also be used to scrub burnt pans under warm water for quick and thorough cleaning.
• Always rinse and dry the pan well after cleaning.

These methods are suitable for most stainless steel, aluminum, and other metal pans, but avoid soaking cast iron pans and avoid harsh abrasives on nonstick surfaces.

If needed, detailed step-by-step guides for these methods can be provided.