"How do you suggest setting up the tarp? How about when it is raining and the ground is wet?"

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. A nice fire on the lee side is a bonus. Of course, if the wind shifts you've gotta get up and reposition. 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...
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OBG