First, let's describe the typical sling. Slings are made of many different materials, but all consist of two lengths of cord, fabric, or hide attached to a pouch in which the projectile is couched before the launch. One cord is the anchor cord, and one is the release cord. The anchor cord attaches to your arm, hand, or finger. The release cord usually has a knot or bulge at the end for secure gripping. The release cord is released to eject the projectile.
The cord should be very strong because a lot of cetrifugal force is exerted during the twirling of the sling. My slings use a matierial that I have found to be very sufficient. I tend to like small diameter cord or leather as drag force is reduced allowing for greater twirl speed. I also prefer smooth cord as opposed to rough ropes and fibers-- the release goes much more smoothly and the sling cords become less intertwined. Reload time and accuracy are very much affected by the texture of the cord. Please realize that the key to developing prowess with sling is good repeatability-- meaning that the sling should function the same way every time you use it. Cordage with random fibers sticking out can only diminish the chances for you to have a successful experience.
The pouch for the projectile is also a key component in you success. The pouch should be very wear-resistant as it has a tendency to brush the ground as it is swinging. I have had the pouch hit the ground with enough force for the rock I was throwing to pierce the pouch. As a first choice, I use leather. I think I've heard of others using fabric, but I beleive this is dangerous since as all fabrics are generally woven. Woven materials tend to fray. Dangerous. You don't want a stone going in the wrong direction in excess of 100mph when the fabric gives way. Some tightly woven and thick weaves are appropriate, however. Doing research you find many primitive slings of the thickly woven type, but quality is a must when using weaves. Certain synthetic bands and fabrics may also be used.
One way that you can learn to make a sling is to purchase one of the slings that I offer at this site. You may copy the construction and design. It's a simple and proven design that I've developed. The knots used to attach the cords to the pouch are simple but specific. I wouldn't use any ole knot or hitch.