While it is cool and unplugged, scrub it with a damp magic eraser, works great, no other products or chemicals needed.
Is the bottom stainless steel, or teflon? Gentle scrubbing with water and an SOS pad will remove burns from stainless steel, but will damage teflon.
Iron some salt on a cloth
Make a paste of baking soda and water, then carefully polish the bottom of the iron with it. Use a damp cloth to remove any residual baking soda, then dry carefully.