Now, this is usually something that the user with do to get out of something. Most likely, dressing like a con man or a woman, etc. will usually distract the enemy long enough for the person to get away. Appearance also matters in case the character has an identity crisis, so they'll adopt an (or multiple) alter ego(s).
Di'angelo, being the most common user of this, has a few short cuts for this. He'll usually either pop on screen wearing the outfit already or it'll come on by itself out of nowhere, confusing the other characters. However, this is never explained fully. He'll also do things manually by waving his paw in front of himself or putting the outfit on himself, though this is barely seen. He can also recolor himself by touching a specific spot and it'll be the color of his choosing. He can also condense and enlarge parts of his body, too (this being seen the most in the episode where he was teasing Domino).
Main Article: Di'angelo's Alter Egos
Most of the time, Di'angelo changes his appearance to suit one of his many alter egos. His alter egos aren't always good on his part, though. In King of Everything, when Erasi puts the crown she cursed on him, he becomes an evil, egotisical jerk. Even though he seemed alright to himself, he ws hurting everyone around him, changing into each one of them and pretending to be them, without anyone ever noticing. No one seemed to be able to cure him except Riggles. In the fanon, The Warden, he actually becomes evil and insane after being that alter ego. Believing that he is actually The Warden, he believes he has to arrest and incarcerate all of his friends and family, even though they've done nothing wrong. After a while, he makes Domino be his "Jared", to which Domino reluctantly does, so Di'angelo wouldn't harm him in that state.