I consider myself an aspiring position shooter.  I have no claim to any fame and post this as an act of sharing with you the training I've received from some freakishly accurate competitors. 

Natural Point of Aim.  If you will, first put up a target of some sort.  You aren't going to shoot it.  It will just be there for this and other exercises.  I just put a small dot about the diameter of a wooden pencil on a sheet of paper and tape it to my hutch.  I get 8 or 10 feet away and stand facing approximately 90 degrees to the right of my target. (I'm a rightie.) It doesn't have to be exact because you are going to have to tweak your stance to get your NPA to have you efffortlessly pointing at the X ring. 

It is important to place the same part of the stock on EXACTLY the same place on your shoulder EVERY time.  Bring the rifle to your shoulder and address the target in an offhand position.  With your lead hand near the front of the trigger guard it will be easier to rest your leading elbow against your ribs and/or hip so that you aren't supporting the weight of the rifle with your leading deltoid.  Now aim at the dot on the paper.  Now that you have done that stay ABSOLUTELY STILL AND CLOSE YOUR EYES FOR THE DURATION OF 3 BREATHS.  Now open your eyes and find out where your Natural Point of Aim really was.  DON'T MOVE YET!  Lets say that you found the NPA was too low.  Move your rear foot further away from the target WITHOUT moving your lead foot.  If your NPA was too high you move your rear foot closer to the target.  If your NPA is to the right move your rear foot to the perpendicular right of your line of sight.  If your NPA is left you can move the rear foot to the left perpendicular to the line of sight. 

Even if you have the crosshairs of your scope or your front and rear sights lined up perfectly on the x ring, you will hit to the right if your NPA is to the right.

My practice goes like this.  Address the target to my left.  I look down at my right shoulder and I bring the bottom point of the buttplate of my rifle to that little hollow where my deltoid, pectoral and collarbone come together.  The muzzle is pointed upward in the direction of the target and I place my left hand or fist under the stock and let my left upper arm and elbow come to rest against my ribs and hip.  I keep my right elbow rather low.  The more I would raise my right elbow the further out from my body the elbow would be and my elbow is not weightless.  Extending weight outward like that will cause you to sway.  I bring the stock to my face and not the other way around.  If you bring your face to the stock you will be leaning your head over and your head is heavy.  If your head is not directly over your center of gravity it will cause you to sway.  Now I have to take the weight of the rifle into consideration in terms of my center of gravity.  The rifle is essentially in front of you so you need to arch your back and let your hips come forward a bit.  Your lead hip is jutted in the direction of the target to better support the lead arm, the back and hips, head and rear arm are positioned to minimize swaying.  That is a drill.  Just getting the rifle to your shoulder and getting a grasp of your center of gravity.  Give yourself some time in position to see if you are swaying on a line perpendicular to your line of sight.  When you learn that feel for getting a "no sway" body position you can then do the next drill.  Here you address the target and mount the rifle to your shoulder and aim at the target.   When you have the sights on the target, close your eyes for a period of 3 complete breaths then open and evaluate and correct your position.  Don't point the rifle with your arms and hands.  Point the rifle with your body position..

Now add dry fire.  Even if your rifle can't be dry fired you can pull the trigger without cocking it.  The trick is to get used to pulling the trigger without disturbing the sight picture.  If your rifle is capable of being dry fired it's even better because you can see what you are doing when the trigger breaks.  After I pull the trigger I hold my position for follow through and then bring the gun down to a rest position for about a minute or so and do it all over again.  10 shots takes 5-10 minutes.  At first it is brutally boring.  When you do it every day for a week or so you will get a tolerance for spending time at it. 

OK, this is a start.