This is sometimes called foxing. The best way I know requires bright sunlight, so this time of year is not ideal, but use a fresh cut lemon, and rub the juice into the spots. It doesn't really work to use bottled lemon juice. and set the pieces in the sun for several hours. I had a dear friend who dealt in vintage clothing for years in NYC, and this was her trick.
I have also used oxy clean and the gentle cycle, but the lemon usually does the trick.