Do not use a steel wool scrub pad or other abrasive material. Some pots and pans have a nonstick coating on them, and the steel wool will remove this which may lead to rusting.
Instead turn on your gas stove to medium heat and add some vinegar to the pan. Once it starts bubbling, add two tablespoons of baking soda to that mixture while stirring continuously with a whisk or spoon.
Do not cook anything else in that pan at this time because the alkali from the baking soda will cause food stains you might have cooked off before to come back onto your clean dishes until they cool down again so you can re-clean them later if necessary with common home products such as dish soap, lemon juice, ammonia, or baking soda.
Continue stirring the solution in your pot or pan till you see everything dissolve into a watery solution that may have some bubbles in it so turn down your stove to low heat and set a timer for 10 minutes. After ten minutes of cooking the solution, turn off your stove and wait five minutes so you can rinse out or wipe out this solution from your stainless steel cookware using a dish rag or sponge with water on it.
Do not soak stainless steel pots and pans in vinegar overnight since the acid from the vinegar might wear away at any protective coating on your cookware. If you want to soak something overnight then use plain tap water instead of vinegar unless you want to re-season that same piece of stainless steel cookware in a year or so.
Do not put stainless steel pots and pans away wet after they have been washed since this will cause water spots on the metal which will oxidize over time from exposure to air and humidity if you live in a humid climate, especially if you leave that same cookware wet overnight. If water spots get baked onto your cookware then use either an abrasive material such as “Bar Keepers Friend” or some baking soda with vinegar on it for more stubborn stains.
If there are still rust stains remaining after cleaning a piece of stainless steel cookware then re-season it by coating the inside of the pan with oil via cooking spray, vegetable oil, melted butter, lard, bacon grease, etc., turn your stove up to medium heat, and cook the oil in your pan inside and out for about 10 minutes just enough for a light or thin brown coating on the inside of that pan.
Turn off your stove and let that piece of stainless steel cooking equipment cool down overnight so you can wipe out any excess oil from the bottom of the pan because it should not be swimming in oil when you re-use it a few hours later since this will make your food taste like burnt oil if it is set too high or left unattended on a hot burner for too long while cooking.
If you have some bits of carbonized food stuck onto a pot, don’t put water into it after scrubbing with an abrasive pad or brush since that will turn the carbon into a red mud that will stick to your stainless steel cookware which you can scrape off later with an abrasive material or pad before re-seasoning it.
If you have really stubborn stains from cooking foods such as strawberries, grapefruit, lemons, etc., especially from cooking them in a pot or pan with no coating on it then add some dish soap and baking soda to the surface of that piece of stainless steel cookware along with a few drops of ammonia while scrubbing that same cookware using a soft brush, sponge, or cloth.
Let that solution sit on your pots and pans for 30 minutes while you’re going about your day doing other things around the house because after half an hour turn up the heat on that solution to medium heat and let it cook for another 10 minutes. If you need to, re-brush or re-wipe that same surface with water and dish soap then scrub again just enough so you can wipe out all of that orange or red swirling swirling away from your stainless steel cookware once and for all.
If there are still stubborn stains left on a piece of stainless steel cookware after scrubbing with ammonia and baking soda then use some coarse kosher salt, rock salt, or sea salt along with more dish soap and vinegar on top of those stains while scouring the inside of your pot or pan gently using a non-abrasive sponge , cloth, brush, etc., in order to smooth out any rough edges left behind by coarse salt or sea salt.
If you have some aluminum deposits built up inside your stainless steel pots and pans then pour in a little bit of baking powder along with dish soap on top of these stains followed by boiling water. If the stains are still there after two tries then take off all the handles from your stainless steel cookware because these tend to be harder to clean than just about anything else, especially if they haven’t been used in over 4 years.
If you’re trying to clean a cast iron pan that has pieces of rust built up onto it then use vinegar on it along with kosher salt before scrubbing that same surface with a sponge or cloth for 5 minutes while running warm water over it as you scrub away those rusty pieces of metal.
After scrubbing away any rusty pieces of your cast iron cookware then re-season it by coating the inside of that pan with oil via cooking spray, vegetable oil, melted butter, lard, bacon grease, etc., turn your stove up to medium heat and cook the oil into that surface for about 10 minutes just enough for a light or thin brown coating on the inside of that same piece. Turn off your stove and let that cast iron pan cool down overnight so you can wipe out any excess oil from the bottom of the pan because it should not be swimming in oil when you re-use it a few hours later since this will make your food taste like burnt oil if it is set too high or left unattended on a hot burner for too long while cooking.
If you have some bits of carbonized food stuck onto a pot, don’t put water into it after scrubbing with an abrasive pad or brush since that will turn the carbon into a red mud that will stick to your stainless steel cookware which you can scrape off later with an abrasive material or pad before re-seasoning it.
In order to make sure your stainless steel cookware is as clean as possible from rust stains and debris from those bits of burnt food then try out this technique on how to make stainless steel look brand new again because chances are if you own any high quality stainless steel pots and pans then they probably cost at least 4 times what a cast iron pan does made out of carbon steel so it makes sense to spend at least half the effort and time throwing a few drops of dish soap and ammonia onto your stainless steel cookware and let that ammonia do all the work for you since that solution eats rust away faster than just about anything else.