I guess 'poncho camping' is along the same lines so I can give some (very) basic tips based on my limited experience.
Location, sleeping pad, and weather are pretty big things to consider.
If you find a spot with nice, level, spongy ground during a nice warm night, you're golden.
If you are like me and camp in rocky areas with lots of unexpected chilly nights, you'll want to make sure your bedding is good. I like pine boughs with a sleeping pad and either a good wool blanket or a sleeping bag, depending on the time of year.
If there's a chance of rain, be sure to pick a spot that isn't going to turn into a stream in the middle of the night and even a mist in light wind can soak you completely in minutes.
Depending on how you set up your tarp, make sure it's well-secured because it may end up with sagging due to stretching or a loose stake/knot.
When you're first trying tarp camping out, bring a backup shelter (small tent) if space permits or at least a heat sheet in case your first attempt is unsuccessful or your shelter falls apart at 2 am. Packing extra layers is a good idea.
Start out in warmer weather, if possible.
Bring extra cordage and duct tape.
This is all mostly based on a simple one or two-sided poncho shelter and I have almost no experience with other forms of tarp shelters so your mileage may vary. I must say that I prefer this form of camping over a tent so I hope you have good luck with it.