Super Smash Bros. for Wii U art
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Super Smash Bros. for Wii U Guide > Basics > My Music

Press Y before selecting a stage to open the music menu for that stage. From here, you can adjust which songs play how often in that stage. You'll find more CD's which will unlock more songs in stages. These CD's can drop randomly during battle, and some are rewards for completing challenges, but the easiest way to get more CD's is to play the Master and Crazy Orders modes. See those sections for more details.

You can also edit the music for the main menu in the options menu.

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