A large part of the game is the fact that you are interacting with your Mii, for the first time ever in a Pokémon Rumble World game. These Miis are sent to other players through StreetPass, SpotPass and downloading through the Internet and are used to represent you. As such, there are a number of ways to customise your Mii using clothing.
Clothing can be purchased in the Shop in the game. You start out with a small choice of clothes before more get added as you rank up. You can also obtain some from achieving certain titles, which then may be later purchasable at the shop if you haven't received it, and recieve gift sets from the King after doing challenges. There are even some clothes which run through the Daily Specials in the shop requiring continual checking for new stock. Purchases can be made via P Coins or Poké Diamonds, depending on the outfit.
Once you have obtained the outfit, you can use it either as your standard Mii outfit, or in your special frame and photo option to be shared with your profile.