If you don't have one of the modern tents described in the other comments, your best bet in windy and rainy weather is to minimize the space you're trying to keep dry to your belongings and yourself.

What I've done is put the tarp down, put my stuff in the middle, and a blanket for myself on one side, then fold it over in a way that water flows off. Then I take a nice long rest until the rain is over.