How can I remove turmeric stains from skin and nails?

Rubbing alcohol works best. Curcumin is the "essence" of turmeric, and it's only soluble in alcohol or oil, not water. You can get most of the stain out with the alcohol, then alternate dish soap (citrus ones seem to work well) or degreasing spray cleaner and alcohol. If you are left with any stains after a few tries, oxy cleaners work okay (try the pet stain pre-treaters) bleach will get the rest. Use a diluted solution (1 tbsp./cup H2O), rinse well, then wash hands and put moisturizer on to replenish all the natural oils leached out of your skin. Or mix lemon juice with a few aspirin, rub it into your skin, rinse. Great exfoliator!