The shoulder carry balances the rifle on your shoulder, controlling the firearm by a hand on the grip. Always keep your finger off the trigger and on the outside of the trigger guard. This is a good carry when walking beside or behind others. It is not a good carry if others are behind you.
When at a shooting range the correct shoulder carry for a break action shotgun would be with the action open, unloaded, barrel pointing down and forward, controlled by both hands.
https://tpwd.texas.gov/education/hunter-education/online-course/hunting-safety/safe-carries