Make a paste with barkeeper's friend and lay it on the dingy spots....rinse.
Don't use straight clorox as it may damage the porcelain.And you can get it "re porcelainized"...those good old tubs are hard to find.

Linda C

Thanks LindaC!!! I know the stuff you're talking about. I'll go try some the next time I run to the store.

Hi, Gayle
If the above advise didn't help much with getting your porcelain bath tub sparkling clean. I have found great success in using the following, product call awesome, you can find this product at any family dollar store, or dollar general, or just dollar store, for only a dollar, this product works great, low price and very powerful,I use it on all my tough jobs when cleaning just spray your tub down and wipe, it's that easy, No hard elbow scrubbing, Now if that don't get all the ring spots, then you will need to get Mr. Clean easer pad, use both, now the awesome can get a little strong when spraying so you may want to get a mask for any harmful fumes, by using the two products I have listed above you want need any other cleaning product to clean your tub.