When fighting in training or duel modes, you can change your character's costume by pressing B so that you will turn to the question mark. Then, press A to choose a character. They will have different costumes. For example, Piccolo will look like Nail and Gohan will fight in his father's costume.

To change costumes, go to the character and press Up or Down. You will be able to select a different costumes. Some characters may have three choices but most have only two.