Most of us use scopes for still target shooting. We're shooting at a 3" circle 40 yards away and sit in a "turkey hunting position" without any rest except by using our knee, just as you described. About the only difference is that we sit on low boy stools and do not lean against anything (like a tree) when we're turkey hunting.
Getting steady is always the challenge. Most of us use variable power scopes set on the very lowest setting. The higher the setting the more movement that you'll notice.
Relaxing, breath and site control, along with a gentle press of the trigger straight back and lots of practice really help. I'd suggest that you dry fire your gun to practice. If you're uncomfortable shooting your gun with an empty chamber, you can use snap caps. Dry fire will help you remember to squeeze the trigger and also help you to keep from developing a flinch as you practice.
Good luck.
Thanks,
Clark