Positive behavior is learned. Make sure you model the way you want your child to act. As an example, if you want her to be quiet (talking in whisper voices instead of yelling voices) during a movie at the theatre, talk to her before hand that when we talk loudly or chatter during a movie, other people can't hear and it is annoying to them to listen to children talking while the characters in the movie are also talking. Mommy and Daddy are not going to talk during the movie and we expect you not to either. Then stick to it! You could also talk about one of their role models and how they would behave. For example, Princess Cinderella talks in her quiet voice when she is out in public.
Reward positive behavior and discourage negative behavior. For example, have an incentive, like a small gift, for good behavior. If your little girl talks during the movie, she does not get the incentive. If she is quiet for the first 30 minutes, she gets to her very own popcorn. After she eats the popcorn, if she speaks in whispers for the next 30 minutes, she gets a small toy after the movie, etc. Set clear expectations before hand and then stick to what you say. If she doesn't "earn" her prize, don't give it to her. Make sure you have set realistic goals for her to reach so she can succeed and learn that good choices lead to positive reinforcement.
Many parents have a hard time taking their young children to the grocery store. Kids get bored, wander off, and get in trouble. A great way to keep them occupied and engaged is to give them their own list (if they can read) or have them help you pick out items you need. Next on our list is apples, which apples do you want? Then have them get a bag, fill it up, and put it in the cart. You would then say, next will you help me find the aisle that has birthday cakes? After shopping, let your kids unload the cart and help bag the groceries so they are not asking for the candies that grace the sides of the checkout line.
Restaurants are also a dreaded outing for parents with young kids. Usually kids act out due to boredom. A child's attention span is extremely short. Again, set clear expectations before arriving at the restaurant. Model correct behavior yourself and tell them what their "hero" or "princess" would do in a like situation. Explain that they are expected to act as a princess would at the restaurant. Bring quiet and activities for them to occupy their time and involve them in your conversations so they don't get bored. If they have bad manners or cry out and act up, take them out of the environment. Go out and have them sit in a time-out for one minute per year old they are. When they calm, tell them what you expect and take them back in. It will only take a couple times for them to learn. Most kids will be so shocked and embarrassed that you actually took them out of the environment, when they get back, they will not want to act up again. For good behavior, you will want to reward them immediately with descriptive positive praise and affection. Say something like, "You are being so good at the restaurant! You didn't even cry and scream once. We are so proud of you and know that we can take you to do special things in the future because you are acting so grown up!"