To start with take a long strip of fabric and fold it in half. I pinned it every couple of inches to help hold it in place. I used a piece of fabric about 20 inches long and 3 inches wide and that made a 3 inch diameter flower. (Also, don't worry if your fabric frays as no one will see that edge.)
Next I set my sewing machine on the longest stitch setting with spacing the farthest apart. I sewed in a wavy line from one edge of the fabric to the other back and forth the entire length of the fabric. My waves were probably about 3/4's of an inch apart. I wasn't too worried about being to consistent with the wave pattern. You could do this by hand and just do a simple slip stitch back and forth.
If you are using a sewing machine and you have reached the end, tie a knot with your strings. (Do not back stitch to finish it off.) Then take the loose string from the opposite end and gently pull gathering the fabric up. Do not pull so hard that you break the string. But you can gather the fabric as much or as little as you want to reach your desired look. I pulled it close to tight but not completely.
Once you've gathered the fabric all the way I slipped a needle onto the end of the string that was loose from gathering the fabric. I then, started at the end without the knot and coiled the fabric around in a circle. Make your circle tight at first and arrange it so the frayed end of the fabric is down and towards the center; this way the folded end of the fabric is up and on the outside. Every so often I would stop coiling and stitch the frayed ends of the coiled fabric together to hold it in place. Once all the fabric was coiled I continued to run the needle and thread through the frayed ends to hold the flower together.