How do I erase the save data on Elite Beat Agents for the Nintendo DS?

It's in the manual on page 11 but just in case you didn't get a manual with your used game :

1. Launch the game wait for the screen with red Nintendo letters on a black screen.
2. Then press AND hold the L, R, A, B, X, and Y buttons all at the same time.
3. This will give you the option to erase the saved data.

Some games provide a button combination pressed on the main menu or title screen that allows you to erase all save data. It is usually in the instruction manual, or you could look it up.

(Usually, a soft reset refers to a way to power off and on the game console easier than sliding / pressing the power button.)