For example, I have seen someone with the music note symbol, and I'm confused on how to get these, because I want them.
Open the Mii Creation.
Under "User Settings" choose "View/Modify user information", skip the body editing and you can change your nickname.
Now, if you press the small keyboard icon (near "z") on the keaboard on screen you can access every special keyboards and characters.
What you're looking for is under SYMBOL:
In the third page you can find the musical note character ♪.