Skin the potatoes if you want. Slice them.

Boil them (or put them in the microwave for a minute and a half). When they are soft enough for a fork to slide through easily, but still hold their shape, take them off the heat and drain all the water.

Take out a portion for lactose intolerant. Add soy milk.
Mash them, adding butter for taste (if it's unsalted, add salt now too), then milk to finish off the smooth texture.

Salt to taste.

If there's sour cream and shredded cheese, take that out too as sides.