The debris you use is whatever material you can scrape up in your local environment. Grasses, leaves, pine needles, and general litter from the forest floor (including dirt and small rocks) can be used. It is best if you can gather long grasses to put a final layer on top to help shed water.
Basic Debris Hut
The debris hut at its most basic is simply a pile of whatever dry material you can scrounge up. The pile must be big enough for you to burrow inside and be insulated, not only from the weather but also from the ground beneath you.
Think about that really big pile of leaves you made as a kid. This is the idea. If you have readily available material, it will be one of the quickest shelters you can literally scrape together.
A Better Option
If you have the time, a more substantial debris hut can be constructed. A simple lean-to or small A-frame is constructed and covered with small sticks. Then the debris you gather is piled on top to form the (hopefully) waterproof cap. If it leaks add more material.