The lean to that is illustrated is not steep enough to not leak in even a light rain.
These old military manuals are pretty good but you need to get out and build one and spend the night in it. I carry a small piece of ripstop nylon in a day pack when I go out. it is only ten by ten but it will build a great sun or rain cover.
The debri shelter that is shown is practically worthless in use. You will do better to put leaning pole around a sapling and start piling stuff on it. Make it as steep as you can and it will turn water pretty good.
If you are making a debri shelter you need to remember that steep and deep means dry and warm. Keep piling shit on untill you don't have any more time to do so. You cannot get enough between you and the outside.
People forget that it is as important to keep off the ground as it is to keep out of the open air and rain.
I like to carry a bag made out of rip top nylon that I can fill with stuff to make a bag to sleep on. Neither the bag or the "tarp" take up much room in a day pack. In fact I keep them in zip lock bags. Avoid mistakes in the woods and carry a little day pack. It will save you gobs of suffering.