How to make your porcelain sink look better than brand new. This method takes a few steps and some elbow grease, but it made my 70 year old stove look fantastic.
From How to Revive the Porcelain Finish on your Antique Stove, New Revised Edition by Jack Santoro (with comments and edits by Michelle)
Oven Cleaner - liquid or spray
Sponges and clean cotton rags
old tooth brush
wooden tooth picks
Rubbing and polishing compounds - I got 3 different 'levels', coarse to fine
WHINK rust remover - a liquid used to remove rust stains from cloth
colored car wax - if your sink is white, get the stuff for white cars
409, Simple Green or other cleaner
Spray bottle with water
I'd do one side of the sink and then the other.
Step .5: Clean the sink out using the household cleaner so the only dirt left is the stuff we have to work to remove. Rinse well.
Step 1: rust stains. Follow this exactly or you will etch the surface of the porcelain like I did on my stove. Then you will cry, like I did. Then every time you look at it you will only see the nasty spot you ruined, like I do. Use the wink with a paint brush or tooth brush and rub it into the rusted spots. Do it carefully and as you see the rust stains disappearing rinse it off. It's better to do this ten times in a row than once and leave it on too long. Rinse very very well.
Step 2: Oven cleaner. Coat it down well and let it sit for 15-20 minutes to get the discoleration out of the scratches. Don't let the cleaner dry or it will be a pain to get off. Rinse. Dark spots and discoloration should be gone or lightened. Repeat. Rinse. Repeat as necessary. Use a sponge or toothbrush to get it into corners or scratches. If you have stains on the side of the sink, you can saturate a cloth with oven cleaner and then tape it to the spot like a bandaid. Leave for an hour or longer. Make sure it stays wet. I found that the ultra cheap oven cleaner from the dollar store actually worked the best, though the stench was horrible.
Step 3: Deep scratches. Use polishing compound and water to buff the scratches. If you need more 'bite' use a little powdered pumice. Don't go overboard here or you will go right through the finish. You just want to make the scratch less noticeable by removing the rough edges.
Step 4: Etched areas. Use the polishing compounds to smooth it out. It will never exactly match the sorrunding area, but it will make it less noticeable.
rinse rinse rinse rinse rinse... and then rinse again
Step 5: Making it shine. Use white cloth and rubbing compound apply the compound using small circles. When you feel the cloth start to 'drag' spray some water on the spot to re-wet it. Add more compound as needed and work your way around the sink. As you work you will see a 'sheen' start to appear, take a clean dry cloth and wipe the residue away and the finish should look great. When I did this with my stove panels I started with the coarse and worked my way to the fine compound. It took longer, but it made a difference. Don't go overboard on the coarse though, you'll add scratches that you have to remove. When you are happy with how it looks rinse well.
Step 6: Keep it shiney. Once it is nice and smooth from the polishing, use colored car wax to seal it in. Follow the directions on the container. Of course, you don't have to do this step if you don't want to, but it sure does look great.
This sounds like a TON of work, but I did all of my stove panels in a few hours, and I guarentee you that was 2 times more surface area than your sink.
Inside me is a thin woman trying to get out. I usually shut the bitch up with a martini.