The sling has been used as long as we have had the concept of tools. It probably predates the bow, but we can't be sure. Slings were a staple of soldiers and hunters the world over. Ammo was plentiful and slings were easier to make than bows.
Construction
All you need is:
Tape. Duct tape is fine, but medical tape works better.
Rope. 3mm Paracord is the best in my opinion, but anything somewhat strong will work.
Disclaimer: Sling are weapons. A sling can deliver more stopping power than a .45 bullet.
Contrary to popular belief, swinging a sling around like a helicopter is a good way to hit everything but what you're aiming at. The power comes from a snap of the wrist, not spinning intensely.
Don't expect to become a sharpshooter overnight. Go to a beach with pebbles, as far from anything breakable (including people) as possible, and propel rocks into the ocean/lake/river.
Once you can sling without killing everyone around you, aim for floating logs or something. Don't aim for boulders, the rocks will bounce back at you.
Place the ammo in the pouch, and hold it there with your left hand.
Pull the sling tight between your hands, and hold it over your head
Let go of the pouch and let it make a circular motion behind your back
Snap your arm forwards and let go of the knot at the right time. Too late and it'll hit the ground next to you, too early and it will go straight up. It takes some practice to get the timing right.
Other styles
There are dozens of styles of slinging, all slightly different. This is the first one I learned, and the easiest in my opinion. Another easy one is the sidearm style. In this video they add an extra spin for more power, but you don't really need to.
Experiment with different styles and find which one suits you.
Links
Slinging.org is THE best resource for all things slinging. The how-to section has tonnes of different types of slings, slinging styles, and even homemade bullets!
ziq OP wrote