There are several cutting methods one can use to cut onions and vegetables. Dicing is the method that produces small, cube-shaped even cuts. Different preparations require different sizes of dice.
To dice an onion, start with cutting it in half, then cutting it lengthwise, then cross-wise until you an even pattern. Lay the onion down and cut it across, to produce small dices. A similar method can be used for cutting other vegetables such as carrots. First, split the carrot and julienne it. At that point, cut across to form small dices.