welcome to my very first instructable:)
It's gonna be simple, short and sweet (for your sink, your hands and the environment).
What you gonna need is
1. Stained kitchen sink (I only tested this method on a stainless steel kitchen sink).
2. Washing up sponge / cloth (something softer than steel to avoid scratching)
3. Fine grained ash (from a wood buring fireplace, oven etc - WOOD only).
3a. Gloves may help to keep your fingernails clean.
What you gonna get:
1. Shiny kitchen sink
2. No chemicals in your greywater (it can be reused for watering with a benefit to the plants)
Disclaimer - it's been proven to work with no damage on my old stainelss sink with numerous scratches done by plates, utensils etc. If you want to try it on a brand new, spotless sink, you might want to test it first on a small area. You are using this method on your own responsibility.
Step 1: Grab a Bit of Fine Ash on a Wet Washing Up Sponge
You don't need too much of it, and it's gotta be really fine powdered ash.
(I think the lightest and finest ash stays atop the ash pile).
Just as much as gets stuck to the sponge is enough.
(Waring - please handle only ash which is well cooled down!)
In the pic below I take it directly from a wood buring fireplace, all nicely cooled down. The ash in the upper left corner seemed to be very fine.
Step 2: Clean the Sink With an "ash-paste"
a little bit of moisture plus ash and there you go, you get a muddy paste which you'll spread around the sink.
(The drain area tends to be the dirtiest so you can give it an extra rub.)
When you think it's done, remove the sponge from the sink and you can rinse the sink.
If it's not up to your quality standards you can continue cleaning, quite likely the sponge will still have enough ash on it to proceed (if not, go to step 1).
If it is clean enough you can leave it to dry.
Step 3: Polish Your Sink
Polish a dry or nearly dry ink with a soft cloth.
It's probably the best part now -
and enjoy your stunning, shiny kitchen sink (no harmful chemicals used and purchased).
good luck with your sinks:)