It's called the SHFFL (Short Hop Fast Fall L-cancel). First, lightly tap the jump button (or press the control stick up very quickly, but this is not recommended). You'll notice that your jump does not go nearly as high as a normal one. Then, either immediately or waiting for the peak of your jump depending on the situation, do an aerial attack, preferably with the C-stick so you can control the direction you move with the control stick. At the peak of your jump, press down on the control stick to make yourself fall faster. Finally, press L within 6 frames of hitting the ground (1/10 of a second) or the frame you hit the ground to half your landing lag. This only works when you're still in your attack animation, so if you do an aerial far above the ground you probably won't need to L-cancel.
It will take a lot of practice. For more detail, please check the stickies on the Melee General Discussion forum. Also, for future reference, always look at those and post in the Q&A thread on this board for small questions like this.
Since you've already made the topic, feel free to ask me a few questions, but mostly all you can do is practice.