You would need to have bought one in the shop or keyed in all the secret codes and got the last rare/secret gift - the costume.
Go to the Games section
Select Items
Scroll through until you see the costume
Press B to select/confirm your choice
Enjoy!
PS It wears the costume all day until bed time - you can't take it off unless you re-set the clock to make it sleep, then turn the clock time back to wake it up again (costume-free)