Bring Yoshi into a level with Berries, and you must be either Caped Mario with a Fire Flower in reserve, or Fiery Mario with a Cape Feather in reserve. Position Yoshi's mouth directly underneath a Berry, and then press Select to drop your item in reserve. Time a jump so that Yoshi's mouth eats the Berry at the same time that Mario collects the item in reserve, and the game will freeze up. You can press Start then Select to exit the level if you've already beaten it.

There is a cool variation of this glitch that not only freezes the screen, but increases your Coin total forever, eventually giving you 99 extra lives. This seems to happen when the item in reserve is collected a fraction of a second after Yoshi's mouth touches the Berry. A good place to practice this is in Yoshi's Island 2.