Which side should a person carry the walking stick?
Normally, regardless of whether he or she is right or left-handed, a person should hold the walking stick on the side opposite their weakened leg, foot or hip.
As he or she walks they bring forward their weakened leg and the walking stick simultaneously. They then bring forward their healthy leg, which takes up the weight of the body, and so on.
When a person needs a walking stick to keep their balance, he or she must do what seems best for the body and find the most comfortable stance.