Probably the best off hand shooter in history, (at least he set the record in ISU Offhand shooting some time ago and it still hasn't been broker) is Gary Anderson, Olympic Medalist. He's still active in the CMP Jr Programs and instructs the CMP GSM Master Instructor Course.
Building the Position:
Feet natural comfortable width apart. Normally shoulder width.
Turn the body (line up the feet) 90 degrees from the target. This centers the rifle over the hip, (left hip for right handed shooter).
The support arm (elbow) rest on the side or hip. You want bone support, not muscle support.
Head straight, bring the rifle to the head (to line up the sights with the eyes, without bending the head or neck)
Support arm, wrist & hand varies to get the elevation needed to get a good natural point of aim. Meaning, you may have to extend the fingers to raise elevation, or go to the palm of the hand to lower the rifle. You can get slight elevation by moving the support hand back and forth on the bottom of the stock.
Windage for the Natural point of aim is obtained by shifting the feet where as you close your eyes, dry fire a shot, without moving open your eyes to see if the targets are lined up with the target (natural point of aim). In adjusting the feet, you can go a bit over 90 degrees but not less than 90 degrees.
Some people look like they are resting the rifle on the chest. If you can do that great. Be careful about weird arched back positions. You'll tire easily and you can't shoot if your lower back muscles are screaming in pain.
Hours of dry firing will build up those muscles.
The right or shooting elbow (if shooting right hand) hangs naturally.
Relax your body before shooting. Muscling the rifle won't make it steadier.
Don't overly grip the pistol stock with the shooting hand, the harder the grip the the harder to squeeze the trigger without disturbing the sights.
Follow through is critical. Most people try to muscle the rifle, holding it up and relaxing the instant the shot is fired. Instead, act as if you are shooting rapid fire and need to get back on target as soon as you shoot. This develops muscle memory that helps with follow through. Sub-concisely you are holding the rifle in the center of the target instead of wanting to drop the rifle.
As others said, dry firing is critical. But as you build your positron dry fire with your eyes shut, after the shot breaks open you eyes to see if you still have you natural point of aim, if not, adjust.
The sight movement in offhand is normally a figure sideways figure 8. Don't try to hold the X-10 ring, instead hold the black, even drifting into the white. Trying to hold an X ring will cause you to jerk the shot.
Relax, accept the hold you get, as you dry fire and practice that hold will naturally become small. As you start out, try shooting for "8"s, you'd be surprised how many hit the black. Again, with practice & dry firing the scores will improve if you stick to your rifle marksmanship fundamentals.
Call and plot your shots as you dry fire. Just like shooting, plot every call.
Be honest with your calls and plots. Cheating on your score/data book will not help you or your scores. You're not going to impress anyone by showing your data book with perfect calls and you're shooting 7 & 8s.
I recommend attending a CMP GSM or Rimfire Sporter Clinic to have the MI (Master Instructor) help you with your position which you can build on by lots of dry firing.
A hint on ammo. Offhand is normally shot at short ranges (200 yards or less). There is no need for hyper velocity wind bucking bullets. Load light to keep the recoil down. This will allow you to get a relaxed off hand position with out recoil causing un-do comfort or causing the rifle to jump out of your hold.
The main reason people (including my self) don't have good off hand scores is they are too lazy to put in the effort of getting a good position and dry firing. This is something you can do anywhere and it doesn't cost a penny.
Matches are won or lost on your hind legs, not on your belly. A good 2/3s of your practice should be in the off hand position.
I would highly recommend anyone wanting to improve their rifle shooting, including Off hand spend $6.95 for the AMU's International Rifle Marksmansip guilde from the CMP.