Any parent who wants to make a change to the approach with our children needs to talk with them about it and set up a clear and understandable structure for them about what is going on and what to expect. We also have to prepare ourselves for the kids to challenge and test the new waters. If we say, "I think we have enough hitting (or yelling, or whatever you are trying to get away from) in the world and I want us to work on avoiding it here in our home." Then we are making the child part of the solution and privy to the goals. It is crucial that we make a commitment to them about what we are going to do. Afterall, we are the adults and most capable of controlling our emotions and reactions. "I'm going to do my best not to spank (yell, scream, whatever you are changing) anymore. I need you to do your part not to hit others (yell/scream etc...) as well."
As parents trying to make a change we need to set up a clear expectation with them about what will happen with the make good choices (have good behavior) and what will happen when they make bad choices. By taking a new approach, we are not swearing off discipline just a certain type of discipline. Take some time to identify (involve the child if old enough to talk) what they like and what they dislike. Is the child over the moon at the thought of a trip to the park and unhappy when he/she doesn't get to watch TV? Does my kid like stickers, trinkets, particular foods and abhor cleaning their room, missing out on a bedtime story or losing a favorite toy? Those things are the leverage. They differ with different children and families of course, but there are things our children care about, things they don't want to lose, and rewards they would love to receive (with the possible exception of some brain or personality disorders. If you suspect a disorder is affecting your child's behavior or reactions to you then please seek medical advice to determine what is best for them.)
In our house, we are trying to use a positive reinforcement model known as the Token Economy and we only move into punishment/punitive measures when our kids have had extremely bad behavior or have lost all of their opportunities for rewards for the day (many proponents of non-violent parenting believe that all "punishment" is the basis for violence and shy away from it. I respect that opinion, but disagree.)
We set up a rewards jar in the kitchen and every morning during breakfast we put three things in. Examples: small candy, collector's cards, small trinkets and toys the sort you can buy bags full of for a few dollars or pickup at a yard sale, and cards to be used as vouchers for TV, riding the bike, playing with bubbles, bubble bath for play only- no washing required, trip to a pool, backyard sprinkler time... all the stuff we would probably do anyway, but we tie it in with behavior. J Bean is 4 and we have another level to the system where she can earn stars on a board we keep on the wall for "meta-prizes" (backyard camping, trips to museum, fairs, etc...). She only gets a star on the board if she keeps all three rewards for a day and she needs 15 stars for a big prize. It keeps us engaged on choices as she picks out her rewards in the morning and receives them after supper. It's a handy threat when things start going awry. There have been days where she lost everything and continued on the spiral of bad behavior and at that point I start taking away things (TV privileges, toys, and/or threatening early bedtime or extra naps).
Even with our system, we still (just like any other parent) have to deal with a completely unreasonable and out of control kid at times. This is the part where I sometimes fail at my goals and get frustrated and react badly, but I'm working on it and getting better all the time. When I realize J Bean has stepped into the alternate world of "Mad." the first thing I do is give us both a break (or timeout) as some people call it. I'm not looking for her to put her nose in a circle on the wall or sit quietly in one spot so much as just get out of the situation and cool down a bit. I make her do that in her room. I used to try to tell her where and how to sit and not to touch toys, but then I'd end up having more confrontation with her instead of giving her the chance and space to cool her jets. Now I just send her to her room (and sure, there is sometimes resistance to that, but I never relent on that order even if I have to carry her in and hold the door closed afterward). We can't get past the tantrum and address the behavior and events leading to it until they calm down. They can't hear or be reasoned with if they are blowing their gaskets. Many people disagree with this part and will point toward how yelling or spanking at this juncture can bring about obedience. I agree that perhaps it will bring about silence and an end to the tantrum, but it will not resolve the problem long term and will not foster trust and open communication with your child. We don't need to establish dominance, this is a person, not a pet, and we are many times larger than them in most cases (plus we have the access to the TV and the snacks). As parents we are obviously the alpha dogs) in the situation. If we let our need to assert total and absolute control then we are not creating a healthy environment. It may be efficient and it may be easier than other approaches, but it is not the goal for non-violent parents.
If we are able to stick with our commitments and hold our children accountable consistently for their end of the bargain then anyone can move to this approach. It takes patience, self-control and time to get where we want to be, but it pays off in dividends of good behavior and a less aggressive child over time. Finally, I am certainly not the expert or the "go to guy" on this topic and I struggle with my own approach on occasion, but I can vouch for the fact it works and that I have well-behaved children. Sure they can still tyrants, they are children, but I hope that I am leading them down a path to becoming reasonable adults capable of solving conflict without hitting or yelling. Adults who are aware of their emotions and able to communicate effectively their problems, fears and concerns. I may not get it right, but if I can get it right enough that they build on and grow my model of parenting then I know my grandchildren will benefit from it and that if we all take similar approaches the whole world can benefit from it. If instead, I chose to continue with methods of parenting that lean on yelling and spanking as the cornerstones then I can look for my children to most likely continue that cycle as well. It's a personal decision we all have to make, I can't tell you what direction to go but I can say with full confidence there are many effective alternatives to "old school" child rearing.
Below are a few more pages/resources to help with your approach and keep positive in your parenting!