Training in times of non-conflict means that you teach your child appropriate behaviors before the actual potential problem occurs. Many times your child will act in a way that is displeasing to you simply because he literally doesn't know any better. Training in times of non-conflict allows you to teach your child what appropriate behaviors are. It is also a time to work out the "kinks" without the benefit of people watching both of you.
What are some situations you might want to train for? Perhaps you have a friend coming over to play with your child. Training before the conflict would be to tell your child Bobby is coming to play, then going through the motions of what will happen when Bobby gets there. You will greet Bobby at the door and do whatever you do. Then perhaps you will go to your son's room to play. Bobby will want to play with your son's toys. Your son needs to share toys with Bobby. And so forth.
Perhaps you are going to Bobby's house to play. You want to avoid a meltdown when you tell your son it is time to go home. You tell your son what is expected and do a practice session.
Maybe you are going to go out to dinner at a restaurant or friend's house. You can practice appropriate voice levels and manners.
It is possible you have decided it is time for your son to sit more quietly at church. You might have practice church time at home. I once attended a conference where a woman spoke who had 8 children. She had some twins and all of her children had come closely together. She was determined that they would sit on the front row and be good. They practiced at home each day until her children got it.
All training in times of non-conflict needn't be in preparation for social situations. It can be for a happy attitude when it is nap time, clearing dishes after a meal, etc. The point here is that training your child before it is a battle of wills between the two of you will help prepare you both. You can clearly outline your expectations and have that clear in your head. Your child can be informed of those expectations and learn how to carry those expectations out.
What age do you start this? Probably younger than you think. You need to decide what age your child is ready, but know that your child understands far more than he can communicate. Keep expectations and instructions age-appropriate, in both directions. Don't be too hard but also don't be too easy. This is something that can be so beneficial to both you and child. Give it a try!