Basically a tarp is a sheet of plastic, which is tossed over a ridgeline, tied between two trees, walking sticks, or whatever you can find. Unlike the static tents and bivys, tarps are very flexible. Besides the multiple designs, you can decide, whether you want to use a groundsheet or carry a mosquito net.
What do you need?
In outdoor shops, you can find dozens of tarps; industrially made, ultralight and equipped with all the features to settle the needs of the modern backpacker. Correspondingly high will be your expenses. The good news is, if you can't afford that, you can just go to your local hardware store and get a simple plastic tarp. A compromise could be a rain poncho from the army surplus store.
To accomodate one person it should have a size of 3 x 3 m (10 x 10 feet). For your ridgeline you need a cord or a rope of 10 meter length. Parachute cord is approved, but any other stable cord will do as well. Optionally, you can bring some tent pegs, but you can use sticks or rocks as well.
How to set it up?
Depending on, whether you want to be protected from sun, rain, wind or cold, there are various ways to set them up. On the internet, there are a lot of websites, describing the different methods.
The most basic way is the A-frame. You ridge your paracord between two trees, toss your tarp over it and stake the edges to the ground.