First, If your fabric has a hem, cut off the hemmed edge. My wrap had tapered ends, so I cut it straight across. The straighter your cut, the easier it will be to remove the weft threads. (As the photo below indicates, I'm not very good at cutting straight and learned this firsthand.)
With a seam ripper, undo the side seams a few inches (the length you want your fringe to be).
Use a seam ripper or pin to loosen the first weft thread (the one going across the width of the fabric), then grab the thread and gently pull out.
Continue, pulling the threads out one at a time. Yes, this takes a long time, but you'll end up with a big snag if you try to pull more than one thread at a time. Once you get the fringe to the length you would like, you can put a stitch in the side hems to keep them from unraveling further.
Gather a small piece of fringe and knot, continuing in evenly spaced increments along the length of the fabric. I held my fabric down with a pin, so I could use both hands to gather and knot and the wrap would stay in place.
After finishing the first row of knots, I separated each strand, placed two adjacent strands together and knotted again. You could also twist these around each other once and knot if you have enough length.
Trim any uneven fringe. The fringe might be a bit crinkly from being woven, but it will straighten out with a wash or just a swish in hot water. You might need to untangle with a comb after washing.
One of the things that helped me get even knots was to wait until I had all the knots done in each row before I tightened them completely. I was able to move the knots up or down slightly when tightening as needed.
Here it is finished!
And here it is in action, with a crumb-faced baby.