Peel and dice your potatoes into small chunks. In a medium saucepan, cover with water and bring to a boil.
Cook the potatoes until they are very tender (about 20-25 minutes). Drain, and add to a mixing bowl.
In a small saucepan or in the microwave, melt the butter, and stir in the half-and-half.
Mix/mash the potatoes while gradually adding the butter/cream mixture. (If you like smooth potatoes, use an electric mixer. If you like chunkier potatoes, use a potato masher.)