the effect can be achieved by getting something like a hula hoop (cut it open) or a piece of small gauge metal rod bent in to a circle. then sew a pocket along the edge of the fabric, like a pair of pants or hood with a draw string. thread the rod or hula hoop through, then do something to close the loop. with the hula hoop, i would recommend a dowel that fits snugly and a screw. for the rod, i recommend a small piece of tubing with hose clamps. affix the ring to the ceiling in the middle of the room.
temporarily affix planks of wood (something like 1x2 pine or thinner) to the walls all around the room, against the ceiling. stretch the fabric to the walls, and use a second piece of wood to sandwich the fabric, clamping it between the pieces of wood. when you have the look you like, screw the pieces of wood together. don't trim the excess yet!
remove the wood/fabric/wood sandwich from the walls, turn the wood 270 degrees, and affix it to the ceiling. to be able to do this, you can strategically cut holes in the fabric that will be invisible when you're done because of the natural creases you have created. through these holes you can screw the sandwich to the ceiling.
once you've decided that you like the look/positioning/whatever, you can cut off the excess.