They should be entered under the "Options" screen off the main menu. Each password changes either Battle Mode or Normal Mode, and after a correct password entry the game will automatically take you to the appropriate mode.

Effect	Password
Allows you to fight all the Normal Mode bosses, one after another.	3879
This changes the configuration of hard blocks and unique items on the levels in Battle Mode.	0413
This displays the so-called "good ending" that you get after beating stage 5-I in Normal Mode.	1999
This gives you 9 total lives and increases the time limit on each stage to 8 minutes in Normal Mode.	5656
This moves the start positions in Battle Mode inward by a few squares, and also decreases the amount of open space in the level.	0926
This starts everyone very close to the center of each Battle Mode stage.	4622
This starts you in Normal Mode with 8 bombs, 8 firepower, and 8 speed (the maximum for each). You also get Detonators, the Boot, and the Power Glove.	2657
This turns every soft block on a Battle Mode stage into a powerup.	0110
Unlocks "super" computer difficulty in battle mode. This only needs to be entered once.	1103