Why not take a leaf from a golfer's book? They are numerous technique and advice books on the golf swing. In many respects I find the golf swing analogeous to slinging; there is the issue of release of course, and the swinging plane is different (not for underarm). I play golf occasionally and have read a golf advice book a few years ago (written by Jack Niklaus -excellent). I have very quickly learnt to sling, meerly a few weeks of practise behind me, by keeping this analogy in mind. This works for sidearm, backhand and underarm. As for overarm, I have practised some but I would say it is more like tennis serve.  So here are a few tips tied to golf and how to apply them to slinging:

1) Hip thrust:

 Therein lies the power of the golf swing; The weight shifts from back foot to forward foot as your hips slide towards the target, they then rotate rapidly to face the target, pulling the torso and shoulders round. The more athletic the better.

2)Proper alignement:

  A good golfer will always line up correctly. Consistency in stance is paramount. Same here if basic accuracy is to be achieved. Here is what golfers do: they trace an imaginary line to the target "target line". They line the tips of the feet parrallel to it, with the back foot instep perpendicular  to the targetline (front foot is less important). I think for slinging, the front foot can be in the same direction as the targetline. This helps cushion the violence of the turn and stops the front leg from twisting (hurting ankle, knee and hip). I found this to be the single most dramatic improvement in my slinging accuracy. All things otherwise properly done, the stone leaves perpendicular to my back foot. I will write more on this as there are some subtler aspects.


3)Care in finish:

   The end position of your body does not matter at all with respect to the shot you just made (stone long gone!)   Why care?
It matters greatly for practice (and basically we are always practising -such is the charm of these games...). The position your body takes at the end gives you clues as to what happened during launch. Have my shoulders ended in right plane? Have my hips rotated? Where are my feet? These are the questions I ask myself. I try to find the causes behind every shot, then I have more confidence in praticing in such way or another.
 Sometimes I find the rock takes an utterly surprising direction; I think this may be due to release problems or stone shape. There will be no sign of such a problem in the finish so I do not rely entirely on finish to tell me what happened. But it is quite a good indicator of swing form.
 Maybe you should find what indicates best for you but I have found an analogy to golf; basically:

Shot to left of targetline= hips not rotated  "too much arm action" ,"lazy swing"
Shot to right of target line= athletic swing but arms not synchronised  "slicey"

 Do keep in mind these are merely clues, to keep in the back of your mind. I find a consistent finish really helps you focus for long practising times.

4) Release timing:

 It is a something which put me off last summer when I first gave slinging a go: Are there no ways of timing this thing correctly? It still is an issue I have not totally solved but I have found ways of limiting it.
 I try to integrate it into another part of the movement. My arm extends out totally and at the same time I release, like normal throwing. Then comes another problem: How do I time the extention of my arm? Well... You time it with the rotation of the shoulders! And how do I time that? -With your hips rotating of course!
 As you see maybe I have no real tip here, just practise and feel


Conclusion: Take with a pinch of salt, I am still starting out  And with respect to release timing, that is an added variable not present in golf so here maybe you can help me out.

Welcome, and great first post!

Slinging tends to be a 'bigger' movement than golf (Though my only expierience is really with putt-putt, but I've seen other people sling) and pretty much any other projectile weapon. This means there are way more variables and precison is a reasult of mainly eliminating some variables and, most importantly, knowing your weapon. That being said, there is still some applicable information in there.

Assuming propper form, release timing and ammuniton are the biggest factors in sling accuracy IME.

The first comes nearly entirely down to practice. There are some factors that effect release timing like ammunition weight, unusual sling length, cords being twisted, large release knot, unstable platform (i.e. you slip), etc. But standarizing/ensuring these things don't happen isn't very difficult. When it comes down to it, Years of Practice is the best medicine for poor sling accuracy. Sling accuracy is still possible though, it just takes commitment.

I place my feet and rotate my hips in exactly that way. Placing my rear foot at 90 degrees across the target line and then placing most of my weight on that is the foundation of my throw.

One tip I would offer is not to have a 'death grip' on the release cord. I find that a maximum pressure pinch is quite slow to reverse and release which leads to missed shots. If I check and relax my grip to about half of the maximum and pop my thumb right open on the release, I am much more accurate.

When teaching people to sling I have found that starting with simple slow underarm rotations powered only by the wrist are a good way to start. I get them to deliver several tennis balls low along the ground like bowling and they can release these intuitively. I build in a bit of an underarm swing to develop the concept of the throw and they keep releasing accurately.  When I take them up to a helicopter with a straight overarm throw I dont mention the release at all and they still do it at the right time sending the shot forwards.

@SerpentOfSilverPlumes

 It's important not to slouch, or "collapse" your spine during throw. I find overhand to be slightly uncomfortable for that reason. Pity, as it's quite accurate in horizontal plane! Maybe javelin throwers/cricketers will have tips on how to do it correctly. Also i have a feeling the forces involved in slinging are higher than tennis or golf (or so my shoulder tells me after a few days) so take care... Good idea to find some stretches/warmup exercises.

@David Morningstar

 Yes I agree! I made three "release knots" in a row because I don't want to concentrate on holding the thing! I hold it loosely between thumbtip and second index knukle. It now feels as if the sling opens on its own, at apex of rotation (I would have to video myself to be sure).  

@Dan

 Practise, but practise smart. That is the advise a golf pro will give you.  

 I know there are a couple of things that really help in golf and I am trying to think of how they relate here. This thread is definitly not over, I am just trying things out beforehand: some are obvious, some need longer exploration.

 Just so you have an idea of my current abilities: I practised this afternoon a lot so was able to get some numbers. I put a hulahoop up at ten meters hanging from a tree branch. The hoop is 60cm in diameter. I threw many many stones in groups of five. I avereaged 1,5/5 stones through.
I had a tough time at the start (no hits at all^^), but got a 3/5 group at the end-very satisfying! It was hard to get inrange, I believe this is because most of my previous practise was at looong range (50-100 meters) and you have to acount for an offset angle at short range. Stone shape has negligeable effect here but I took care to choose consistent weight.

 If we do some maths:

D is distance to target
R is radius of hoop
@ is angular accuracy

tan(@)~@=R/D=0.03 radians~1.7°

30% hits in a 2° cone. Not bad? Also a few "epic" hits from longer distances but after many throws...

Hello, I have some more details on alignement. Hopefully it will help for accuracy at all ranges.

 When slamming stones at a bottle ten meters away, or at a tree stump fifty meters further, I align differently.

Lets take the first case: If I position my stance towards the bottle and toss, the stone will in best of cases leave perpendicular to my back foot, parrallel to my stance. The distance between my hand and my neck is roughly three feet and my sling is ~28 inches. The stone will pass harmelessly 1,5 meters to the right of the bottle! (in sidearm technique)
  I actually practised quite a bit without taking this into acount and it resulted in many poor throws to the left surprisingly enough ("pulled shots"). Typical; a poor stance led to overcompensating, and overall week shots.