From J. C. Tate, CDR USN (Ret.) – Distinguished in 1991

A good prone position is a make-or-break position - for one thing 300 of 500 points are prone.  Also, they say you win at offhand and lose at 600.  I can't argue with that either.  And, as you say, prone ought to be the most stable, all bone & sling, no muscle, relaxed position ... if you build a good one.  How do you know if it's good?  When you fire a shot, your rifle will naturally, effortlessly settle back almost where it was before the shot broke.

Of course, that last comment applies to sitting rapid too.  Which is why I see good shooters spending up to 30 seconds in sitting and 35 in prone rapid, just to build a good, relaxed, natural-point-of-aim position.

That said, here are my comments.  My context is for a right handed shooter.  I am mainly thinking of service rifle/EIC shooting, that's almost all I did.  Also, I shot M1/M14, so recoil was much more an issue than with M16/M4:

1. Get your sling as high up on your left upper arm as possible. (A bit of spray adhesive will help keep it from slipping down.)
2. Put the rifle’s forend on the bones where your hand meets your forearm; your fingers should be ‘floppy loose,’ not gripping the forend at all. Position your support/left elbow as close to directly under the rifle as possible. A perfectly vertical support arm is easy to duplicate. If your elbow is not under the rifle, any amount of variance will move the point of impact; if that variance is not the same, your point of impact will also vary. You may need to roll slightly on your left side to get your elbow under the rifle. If that’s the case, then pull your right elbow closer into your side … if possible, dig it into the ground a bit to help avoid slipping on recoil.
3. Depending on what sort of shooting jacket is allowed (if any) use your shooting/right hand to position the butt well into the chest-shoulder ‘pocket.’ When you then move that shooting hand forward to grip the small of the stock, the pocket will tighten and your jacket folds will grip the stock and help hold it in place. (A little spray adhesive on the butt and on your jacket will help prevent slipping too.)
4. After building this solid position, you will need to refine it to achieve a relaxed, natural-point-of-aim. To do this:
   a. First wiggle your hips to get as close as possible to that relaxed, on-target position.
   b. If your sights aren’t dead on, slide your right foot to the left or right a bit to move the muzzle in the opposite direction. (Try it! This works for a gentle, lateral adjustment.)
5. Three peripheral comments. Practice getting into prone, then getting up, and getting down … until you have a reliable routine. When practicing getting into a good prone position, don’t forget to do it with your scorebook and shooting scope so that you know where to place them for use with little or no movement. Finally, practice dry fire with a helper whacking the muzzle to simulate recoil and consistent, on-target recovery. (On an M1/M14, the helper can hit the oprod to cycle the action.)
   I hope these are helpful. They helped me!

More: https://www.gunpowdermagazine.com/high-power-service-rifle-advice-for-building-your-prone-position/