To make the glitch work, you need to do these things.
1. Plug a controller in port 3. (You can get Master hand to appear on the other controller ports too, but you can't control him.)
2. Choose your characters as normal. (Make sure at least one of the four character selections have nothing on them, that can only be done if there is a controller port plugged into that selection.)
3. Go into the name entry screen the instant you exit it. (What I do is hold the B button, press A on the character name, and go to the name entry screen. If you have a large amount of names, it will be harder using my way. Instead, get a second controller to press B, or the back button in the top right corner. If you do it too early, you go to the name entry screen. If too late, you exit to the menu. If exactly right, you go to the level selection screen. Select a level, and you go to any stage. The empty names will be Master Hand. It works with 2 Master Hands, but glitches up on 3. I haven't tried 4, but I'm sure that will glitch up too.)
4. Control Master Hand with the third controller. (The controls are a bit odd, but almost everything you do doesn't interact with how you play the game as a normal character, which helps when you are using a normal character at the same time as Master Hand, as I do in the video. It works like this.
Hold down either A, B, L, R, or Z, and press one of the D-Pad buttons. for example, L down is the finger walking attack.)