If you go to the equipped home page and scroll down to Tarp Shelters-An Introduction, you will see a lot of different ways to rig a tarp...
I've seen it. It is not very helpful. It's like looking at a dictionary; all the words are there but you still have no idea of how to write a sentence. There are no helpful suggestions of what works best for what situation.
Well, the fast and easy down and dirty way would be to put about 1/3 of the tarp on the ground (to sleep on), and run the other 2/3's up at about a 45 degree angle to block the wind and rain.
It's still a lean-to. You get a ground cloth but I've never seen the wind only blow in one direction. How is the lean-to better than a tube tent to keep you from getting wet?
My son (BSA Life scout, Order of the Arrow and Troop SPL) likes to take a tarp and form a burrito: 1/3 on the ground and then form a tube tent with one end closed.