Iron on the adhesive to the wrong side of the top of the placemat (a 14x18 rectangular piece.) Make sure it adheres everywhere. (Follow the manufacturer's directions.) You can take the paper off now or after you cut the waves.
Next, fold the fabric in half as shown. I placed my ruler at the end of the folded map so that I would have a 1" margin on each end. Then I used my rotary cutter to cut wavy lines from the fold to the ruler. They can be of various widths. You can use scissors, too.
Open up your fabric.
Now iron the adhesive on the backs of the fabric you will be weaving. Remove the paper once you have finished! (I forgot and had to fix it after the mat was woven. Wayward forever!) Cut the strips into varied widths between 1/2" and 2" wide.)
Now start weaving. Keep the strips snug together. Toward the end, you may need to make one or two strips strips narrower.
Once you are finished, make sure everthing looks right. The edges of strips that show should line up with the edge of the mat. Carefully lift the mat and place it on the rectangle you will use for the back of mat. Line up carefully. Now, iron everything very securely. Make sure the edges adhere very well.
Trim the edges with a pinking blade and you are finished!
If you like to sew, you could zig zag around the edges or add other decorative stitching.