Here are two fast made mini-tutorials.

The first one is for the basket sling that is shown on the attached picture and originally here:
http://slinging.org/forum/YaBB.pl?num=1172017416/3930#3930

You need some very long cords, i.e. 9 cords of approx. 3 or more arm spans and 6 cords of approx. 2 or more arm spans, a needle (if possible, a weaving needle without a sharp tip), scissors or a knife and 2, better 3 clips like they´re used in kitchens.  A print-out of the picture may help you when the drawn braiding manual (attached pdf) isn´t understandable.
I hope you can follow my sketches and are able to decode my handwriting. Have fun with braiding.

Braid the (here 9-strand) retention cord including the finger loop until it has the desired length. Divide the strands into 2x4 and keep one remaining strand (the 9th) apart, e.g. by clipping it to the retention cord. 

On each side sew one strand through the holes in an up-down-up-down manner and one strand contrary, i.e. in an down-up-down-up manner. The result is a row of loops flanking the pouch. By the way: the tension of the sewing determines the cup shape of the future pouch. I personally prefer no or only slightly cupped pouches in this type of sling.

Now there are still two cords on each side that have to be sewn on the pouch. This is done by sewing through the loops, for the first cord entering with the needle always from the outside in every loop and the contrary for the second cord, where the needle enters in every loop from the inside.

At the end only one strand remains free.

The 9th strand is sewn under the first pair of loops, whipped around the retention cord, sewn trough the first hole to the inside of the pouch and fixed there by a knot.

Now it´s time for attaching the inner layer of the pouch. Cover the inside of the pouch (= the side with less visible cords, only a row of loops) with a sufficient amount of the flexible glue and attach it to a piece of leather, that on the release side should be ½ - 1 inch longer than the first layer by pressing together. Make sure, that there are no spaces without glue, especially at the margins. Let the glue dry out (I do this overnight).

Cut the inner layer following the form of the outer one, except on the release side where you let a short “nose” that protects the release cord from the ammo. Be careful that you don´t cut the cords.

Finish braiding the release cord, take some stones and sling them.

P.S.: There are a lot of variations, e.g. making both layers of the pouch with or without the central cutout. Another alternative would be starting the braid from the release cord (e.g. with a woven release tab) as a 4-strand braid, then adding two more cords some inches before arriving at the pouch. 2 cords on each side would be used for the sewing through the pouch holes, 1 on each side for the sewing through the loops, coming out with 6 strands on the retention end. For more flexibility on the release end, the 2 additional strands also could be added directly on the pouch´s release end by placing a long cord with its center under the first pair of loops and then sewing back through the remaining loops. 

Wow, great work LakeSlinger!