As a seller of pottery and porcelain pieces, I have found a couple of great ways to reduce or even eliminate the awful staining one can find on older pieces.  These stains are due to seepage through teeny, sometimes invisible (to the naked eye) cracks, called crazing, in the glaze.   First:  DON'T put these in a chlorine bleach.  This may alleviate the problem, but it is also damaging to the piece.   Here's the first (easiest) way:   Go to the store and get some regular oxygen bleach; the kind you use for laundry (OXY, etc.).   All you need to do is mix the powder (in hot water) or just use the liquid kind, and soak your stained piece in this for several hours.  Sometimes, this is not even necessary; you may see results much more quickly than that.   This method is good for mildly stained pieces, i.e. coffee stains in an old cup.  Here's the more involved (BUT effective!) method:   Go to a beauty supply store and buy the Hydrogen peroxide bleach, 8%, the type that is used to bleach hair.   Take the piece and soak it in this, completely submerged overnight.   Then, take the piece out of the peroxide (don't dry it) and place it in your oven set to 200 degrees (or on the WARM setting).  Let the oven rise to 200 degrees with the pottery piece in it.  DO NOT preheat the oven, as the sudden temperature change could aggravate the crazing.   Leave it in for an hour and then wash it.  You should see that most of the staining seeped out with the peroxide when it evaporated during heating.    AGAIN!  DO NOT take the heated plate out and place it directly in cold water.  You may transfer it  to hot water for washing or allow it to cool before washing it.   This has, in my experience, totally eliminated or greatly reduced this staining.   Good luck!