Peel the potatoes. Keep them in a bowl of cold water until needed. If they are large, cut them into quarters.
Put the potatoes in a pot, and add just enough cold water to cover. Cook the potatoes at a slow simmer for 30 to 40 minutes, until they are easily penetrated with a knife.
Drain the potatoes, being sure to save the cooking liquid. (If a thinner purée is desired, the cooking liquid can be used instead of cream or butter to thin the finished purée.)
Purée the cooked potatoes by forcing them through a drum sieve or ricer. Using a drum sieve produces the finest texture and is also the least likely to break cell walls and release starch and thus give the purée a gluey consistency. A ricer prepares a lovely purée (it doesn’t turn the purée gluey), but the purée will still have small lumps that are inappropriate for a sauce. If the purée is being beaten into a sauce to act as a thickener, the sauce should be strained through a chinois to eliminate the lumps. Never use a blender, food mill, or food processor, as these overwork the purée. Season the purée with salt and pepper.