How you grip the firearm, how you hold it in your hands and support it with your body, plays a crucial role in how well you will shoot. A firm grip, but not a super strong grip that you can’t do for a long time will enhance your ability to absorb or withstand recoil and also control muzzle flip.
Using a push pull approach, with the trigger hand or arm pushing against the handgun and the supporting arm in an isometric balance will help stabilize your platform.
Pulling the rifle or shotgun into your shoulder with the shooting arm and using the supporting arm to stabilize the firearm both vertically and horizontally will provide the most stable platform.
Consistently repeating the geometry of this platform, ie, particular configurations of the palms on the handgun, specific way in which your shoulders and elbows are held, even how you place the firearm in relationship to your neck and eyes will go a long way to improving your shooting.
The same can be said of long guns. Where you put your cheek on the stock, how you grip wih your shooting hand and how consistent you operate the supporting arm will have everything to do with how small your group size is.