Begin with a length of (ungutted) paracord. I am sorry I don't have an exact length to tell you, since I didn't keep track, but it ought to be about 8-9 feet to be on the safe side. (You can always cut it down when you are finishing it.) Fold the cord like this. You will be creating five lengths that are doubled next to each other.
This project is done with full symmetry through the center point, so do the exact same thing to both sides. (You can do this one side at a time, of course, but keep track of the strands.) Take the bight that lies next to each working end, and lay it on top of the bight next to it.
"Lasso" around the two bights with the working end. (Make your work look exactly like you see here.)
Tuck the working end (they are short in this example but will be about 4 feet long on a live specimen) over itself and then down through both of the bights.
Here is what it will look like with both sides of the pouch done.
IMPORTANT: Take careful note of that strand that is running diagonally from low-left to high-right. That is your middle-most single strand. When you flip the pouch over to begin weaving the next step, make sure it is the center strand! From there it should be easy to see which are the outer-most and second-outer-most strands.
FLIP THE PIECE OVER. A moment ago, you were looking at the back of the pouch. You will now be looking at the front of the pouch. You can tell one from the other because when looking into the pouch, you will see the working ends coming out of the bights "toward" you.
This section should be at least 4.5" - 5.5" long. (It is shown here shorter than it should be.) You will need to make the corresponding lengths of the strands in the pouch approximately equal in length, but you should be finding that the center-most three will "pouch down" to make a sort of cupping. Play with it. But at this point when I make one, the pouch already seems to "know" which side is the cup. Tighten up the "lassos" that wrap the bights.
Now it is time to start weaving a second strand in. Wasn't I nice to use a highly contrasting cord color? You might as well just start from the left side and poke a short length (about 4") through as you see here (exactly as you see here) so that sticking out to the right is the part that will be the end (as you will see in the next picture). The left side is your working end which will be woven across the pouch.
Now you can see the right-to-left-to-right weave of the crossing (orange) strand. Continue weaving O-U-O-U-O-U... all the way to the other side of the pouch.
IMPORTANT NOTE: It is not necessary at first, nor will it likely even be possible, for you to make these strands snug up against each other and look like the arrangement in a Ladder Rack Knot. As long as the overall shape of this pouch is more or less almond-shaped, it will be fine. Do try to keep it even, of course, but small gaps are not only not undesirable, they are more-or-less unavoidable. With that said, however, based on the fact that an EDCforumite named Nephiel proved just how tight and handsome this pouch can be woven, I revisited my technique and discovered that you can indeed make this pouch look pretty darned neat. It's going to take some effort, you can be sure of that, but it can be done. If it doesn't happen on your first sling, don't even worry. Just keep it, and work tighter on the next one. The first, not-so-tight one will still work just fine. (P.S. Thanks, Nephiel, for showing me the potential of this pouch design!)
This is the pouch when the weaving has been completed and tightened-up and evened-up. Yes, you will have to do a little "working" of the orange cord. Use your fingers to push or pull the horizontal strands along their green warp strands if they seem to be bunched toward one end or the other. Fit as many crosswise orange strands as you can, to minimize gaps in the pouch. It may help to have a titanium "icepick" marlinspike from LCranston, like I do. ;-D
(If you discover that your pouch seems to be longer than you want it to be, you can undo some of the cross-woven strands, and re-work the sheet-bend strands until the length is more to your liking.)
Flip the work over and look at the back side of the pouch. Single out the specific strand that I have picked up with the titanium spike in the picture. Tuck the short end of the orange cord under that strand, and the one beyond it. That should be good enough to keep it plenty secure, although you can always go for a third strand. (Remember, you will do this for each symmetrical end of the pouch, and it will look exactly the same as the first side or you did something wrong.)
Clip the end and melt it according to your preference for finishing paracord ends. Tie your preferred loop in one end of the green cord, and a stopper knot at the other end, and you have yourself a sling! I favor a "Longbow Knot" for the loop, and an "Ashley's Stopper Knot" for the trigger knot.
For ammunition, go to Walmart and check in the home decor area for "decorator accents" and such. I bought a bag of glass droplets that are close to an inch in diameter. They are shaped like bon-bons, or Cella's cherry candies, and nestle perfectly into the pouch. Yes, I would prefer polished steel balls for their additional mass, but they are not cheap! I also find that this pouch works very well with golf balls.
Please use care, intelligence and maturity when using your sling. I of course have no control of, and bear no responsibility for, what you do with your sling. I am only a learning novice, myself. Many thanks to all on slinging.org who give of their knowledge and experience so freely.
Be safe, and have fun!
(Here are some pictures of a completed specimen using UAC paracord, which makes a handsome sling)