Executing the Glitch
The glitch can be executed only in Time, Bonus, or Coin modes. You may set the time to whatever you wish. Next, place the cursor of your controller over the name field on the character select screen. On this controller, press A and B simultaneously. Release A, but hold onto B. Scroll down to the "Name Entry" button. If you press A again at just the right time (the 19th frame starting from name entry prompt appearing), the game will skip to the Stage Selection screen. Select the stage. If it loads properly, the game has not frozen and the player will be in a Single Person Melee.
Under normal circumstances, it is impossible to advance with only one combatant. However, since the Name Entry glitch forces the game to advance, there is only one character in the melee. It will remain this way until time has run out.