When you defeat Bowser Koopa in level eight, level four, you will see the princess. She will thank you, and she will tell you that now it is time for you to move to a more difficult quest. After starting over, you will work on the star worlds. They are the same as the regular worlds, except all of the basic enimies will be replaced by shell enimies. Remember that shell enimies move faster, you cannot shoot them, and you can't tell when their shell will begin to move.
In level 4-2, do what it says to do above. You can warp to world five.
In level 4-2, when you reach the first set of elevators, jump down to the ground. You will see three blocks above you. Walk to the left of the first block, and jump as far as you can. An invisable block will appear. Then, jump right below the last block. Another invisable block will appear. Then, jump onto that block, break the block above you, and jump up onto the three blocks next to each other. Walk to the left, and fall down onto the first block that you made visible. If you fall down onto the bottom of the screen, than just try again. Walk to the right of the block, and jump. A beenstalk will come out of the block that you hit. Go onto that beenstalk, and you can warp to worlds six, seven, and eight.