Hi, Merry Christmas.
People keep talking of leaf debris. In my experience it doesn't work against rain at all. It just acts like a sponge. You might stay dry for the first hour of rain, but by then the stuff is soaked and for every drop of rain that lands on top, a drop falls through underneath!
When I were nobbut a lad, I build a fantastic shelter and thatched it with a couple of bales of hay. It was brilliant, until it rained. Then it was like sheltering inside... a very wet thing. Very wet. And it stayed wet long after the rain stopped.
I'm lucky: I have access to a bit of neglected valley land in Northumberland, so I can experiment. Dead bracken is good, so long as you use it properly. You need to gather it in bundles, with the stalks all pointing in the same direction. If you think it is going to rain, shake it to get rid of the old leaves. They're really good for bulk, and will build a quick roof, good insulation etc, but like leaf litter, just get wet, then drip. Then lay the bracken stalk bundles on the roof, with the stalks pointing up and down, so water runs down the stalks. You have to use a huge amount to get a proper thatch: a whole armful is just placed on, as it is, and don't spread it out. But it works very well, even in very wet weather. And it's easy to gather, though bracken cuts are pretty horrid. Wear old leather gloves. Cheap gardening gloves are good. It doesn't last long: it rots to pretty well nothing in a few weeks.
Reeds are the best: we have a marshy valley bottom with forests of reeds. They don't grow very tall, and they're not easy to harvest, but they have a sort of shiny outer, and shed water like fury, and they don't rot like bracken. I've thatched shelters with this stuff and it seems to last indefinitely.
The idea is to have dense cover of lines of something: stalks of bracken, thin sticks, reeds, whatever, all pointing down. Then the rain falls on the first layer and runs down it, surface tension and all that, before being joined by more rain from the sky, and getting so large it drips down to the next layer, where it runs down again, a few inches down the stalk, before getting too large again... and if you have, in effecty ten layers or so, it never gets through, but goes to the ground.
As someone said, the angle is very important. There really is no such thing as water-proof cover, the best you can get is stuff that doesn't absorb water, like reeds, and will shed water at an angle. A flat roof made of genuine commercial thatch will eventually leak. It really has to be at least 50 degrees before it will shed water and this tends to mean a small, steep shelter. But dry.
Regards