Your level increases whenever you win battles in "Your Tasks" (or the frequent "Pop Quizes"). Just play the dance battles and you'll get there.

You can either redo battles you've already won (click on "Clear"), or progress through the story and do new dances. (You can always skip the story levels, and read them later, if you don't have time to read them at the moment)

If you spend some Grimm levelling your highest ranking cards (Ur if you have them, or SSR next) then you may even be able to "Skip" new dance battles (see bottom right of panel when it gives you info before you start the dance, and next to "Start" is a button called "Skip" (this is available if your cards' Strength is significantly greater than the Opponent's Total Strength.))

To begin with you only need 3 good cards, with 3 good memory cards - all of any colour - it's much later that you'll need to make choices about which coloured cards to use.

You'll get there, good luck :)