I use a lot of the marksmanship principles I learned in the Marines.
Using bone support rather than muscle is a biggie. If you're sitting cross legged, put the back of your elbows in the pockets formed just inside the knees, keep your front forearm as vertical as you can. Also try using the sling to steady your shot, whether you're sitting, kneeling, or standing. It really helps keep the front end of the rifle steady.
Rather than using the palm of your hand to hold the forend, try using the "v-notch" formed between your thumb and index finger, with your palm facing back at your body. You'll notice that when your forearm is vertical, the notch is directly over the bone, so there is next to no muscle being used to steady the weapon.
Shooting at the bottom of the breathing cycle is another thing that helps (no air held in lungs, rather than holding your breath with full or 1/2). Once I have the crosshairs hovering over the target I wait until half of the last breath is out to start squeezing the trigger. At the very bottom of the cycle the trigger is about to break and the crosshairs are settling near the center of whatever I'm trying to hit.
There will always be some movement, but you can minimize it with practice. I love using a scoped .22 LR for practicing shooting techniques because you can take hundreds of shots for a few bucks, and it's easy to see results. I would start practicing with a 5" bullseye at 25 yards or so. Another option is to dry fire, or "snap-in" as we called it. I have used a magazine picture of a coyote placed across the room with the scope turned all the way down and just "shot" at it over and over. You'll start recognizing good shots and also where you're not perfect. This also helps to keep you from flinching when you are live firing.
Hope that's somewhat helpful.