Conventional wisdom holds that pots and pans should be given a good soak. But every metal has different properties and requires special care. Stainless steel is prone to stains from heat and hard water. To remove them, apply white vinegar with a soft cloth and rub. Always dry thoroughly after washing to prevent a film from forming. Never soak stainless steel cookware; this will result in pitted surfaces.
If you don't have a self-cleaning oven (which burns off residue at very high temperatures), try a paste of baking soda and water. Coat the oven surfaces with the paste (avoiding bare metal and heating elements), let stand overnight, and, while wearing gloves, use a plastic spatula to remove it.