Instructions
Advance to level 3-1. The 99 lives trick appears in world 3, level 1. Battle through worlds 1 and 2 in order to reach this 99 lives opportunity.
Battle through level 3-1. The 99 lives trick is at the end of level 3-1. Survive the level until the end.
Pause before the staircase with two green koopa troopa (turtle) enemies on it. At the end of level 3-1, you will see a staircase with two koopa troopa enemies. Pause before this staircase and ready yourself for the trick.
Jump over the first koopa troopa to descend the stairs. The first koopa troopa is not a part of the trick. Jump atop this first koopa troopa on your way up the stairs if you'd like, but it's not necessary.
Jump atop the second koopa troopa just as it reaches the end of one of the stairs. Jump on the second koopa troopa and it will hide in its shell.
Jump repeatedly atop the second koopa troopa's shell. Line up Mario so that he's on the left edge of the koopa troopa shell. Jump repeatedly on the shell. The shell bounces into the back of the stair and back out. Each time you jump on the shell -- and the shell does not fly away from the stairs -- you will earn one life.