The best advise I can give has already been mentioned: practice holding your rifle at the shoulder often. It strengthens the muscles. When I shot BPCR, I kept it in my room. Any time I walked into the room I picked it up, set the trigger, and clicked it (hammer stays down). Make sure your particular gun type allows this without damage. By the time I got to my first match, the routine of picking up the rifle, setting the trigger, holding and firing was totally natural. Of course, I had practiced for years as a kid with a BB gun, then a .22 also. It becomes natural to be a good shot if you do this one thing - shoot a lot, or at least dry fire like above.
^^^ This.
Developing the muscles used in that exact action is the only way to get steadier.
Adding a weight can help develop those muscles. Works for pistols as well.
When doing any particular thing, the more often one does it the better they will get at it, both from the coordination of repeated actions as well as the muscles used gaining strength. Ive seen some truly atrocious offhand shots, part of the equation was they never passed up the opportunity to use a rest. One friend made a horrible gut shot on a deer because he was a horrible offhand shot, he struggled to find a rest to make an easy shot, 75 yards with scoped rifle, couldnt find a rest where he could see it, and muffed it badly. He never shot offhand in practice. He was a good shot with a rest, but its not hard to shoot from a rest.
The majority of my shooting the past 20 or 25 years has been offhand. I figured its the hardest, so should get the most practice time. Where I shoot the best targets are 200-300 yards with a 24" 600 yard plate. A 4x scope on the 600 wasnt much of a challenge after doing it several years, kneeling or sitting seemed like cheating.
Shooting running game is also great practice, running rabbits with a rifle or pistol, or squirrels helps our overall shooting abilities.
As with rifles and practicing the most difficult thing, shooting pistols one handed is the hardest, so I practice it almost exclusively the past 25 or so years. When making a shot on game I use two hands, but again, it almost seems like cheating once one gets the hang of one handed. Most pistol practice is on the 200 yard rocks and 300 yard plate, maybe 80% vs 20% at various closer distances, and stuff like yucca stems and small things up close.
And yes, most rifle shooting has been iron sights. The Colts Patent self loading lightweight army rifle of poodle caliber was most often used, its what was cheapest for ammo at the time i was shooting the most. Many cases of money turned into noise back when surplus was imported without hindrance.
