Before I was ten my Dad showed me his way of making a sling...
Cut out a patch of leather a couple inches wide in the middle and tapering down to about a half inch wide on the ends... total patch length about 4-5"   Tie a figure eight knot in the patch-ends of your chords.  Place the chord on the patch with the knot about 3/4 inch inside the end of the patch.  Roll the patch ends up around the end of the chord and whip the two together... the old Boy Scout manual will show you how to whip a countinuous chord... one without an end.  After whipping the two together, pull the chord as to pull it out of the whipping... as you do so the figure eight knot will wedge into the hole formed by the whipped patch end.  Loop the finger end of the retained chord and whip it also so the open loop just fits your middle finger.  Tie the release end with a figure eight knot.  Play with the placement of the release knot until it lies next to the retained chord right where your thumb and forefinger come together at the same time the patch ends of the chord are even with each other.  For the whipping string use waxed linen or nylon shoe sole stitching... a good shoe repair shop will sell you a remnant roll for pretty cheap.  A little Snow Seal or warmed bees wax worked into the whip coil is also a good finish.

A couple of notes: 
Pulling the chords as they pull when tensioned from a throw will stretch the patch into a cupping shape... no patch stretching with mink oil or other leather treatment is required.
Engineers know about something called "notch sensitivity".  Cutting a hole in a patch where a chord passes through it is a good example of the phenomenae.  Patches will be prone to tear at that point due to notch sensitivity and the high stress concentrations at that point.  The whipped attachment method eliminates that problem because the patch has no holes in it and the forces are distributed around the width of the whipped roll.  I've had a good tough goatskin patch for over thirty years that has worn out about four sets of leather chords and three sets of "accessory chord" (3mm dia. "climbing rope") and the patch shows no sign of giving out any time soon.  Try it... maybe you'll like it.

George N

that's all very complicated, pretty yes, but complicated. I just use a loop at the end of my cords, shove it through a hole in the pouch and feed the cord back through and pull tight. Utterly secure, dead easy, hell you don't even need to secure the loop, the act of pulling it tight does that for you.

Now it may not be aesthetically pleasing - BUT I can easily switch my cords to different pouches, currently got the Aussie on them, but now weather improving I'll be switching back to my small leather pouch again fairly soon :-) 
You can even try different length cords with the same pouch.

I just don't see why you lot have to make it look so complicated :-)

I'll get a picture in the next few days...  to curious_ardvaark... I'm sorry about being complicated but my nature is such that any creation of man is to be improved on and the creator thereof has the greatest responsibility to make the improvements.  I REALLY liked your response idea though as it too would tend to pinch a section of the patch to hold it instead of being totally concentrated at the hole...  BIG THANKS!

ArizonaSlinger,

As it happens, Captain Paul just joined and posted photos of one of his slings,

here

and

here

.  Take a look at how he attaches cords to his pouch.  I think GunsOnWheels is describing the same thing.

what's wrong with loops ? More secure than any other method. Quicker, absolutely no skill in anything other than bending a bit of string into a loop required. And it holds the pouch flat and slightly curved.

:-)