Instructions
Complete Level 1-1. There is no way around this, as you much finish 1-1 to get to the warp zone.
Go through Level 1-2 until you come upon the downward moving "floating elevator." This will come a little bit after the three pipes.
Move past the downward elevator and go onto the island. You will then see an upward moving elevator past this island.
Leap onto the upward elevator. Ride it all the way to the top of the screen and then leap onto the ledge at the top of the screen.
Run to the right until you come upon the hole for the Warp Zone (which will be labeled). Fall into the hole.
Go to the far left pipe that has the number "4" over the top of it. Jump on top of the pipe and press the "Down" arrow key. You will then be transported to Level 4.