1. Talk to them early and often
The biggest mistake I see parents make time and time again, in my opinion, is waiting until they are absolutely sure they are moving before telling their children. Most I believe do it with good intentions- they don't want to unnecessarily upset (or excite) their children, only to have it fall through. I know because my parents did it once. Let me say from experience that it is always better to tell them as early as you can so that they have time to adjust to the idea! I say this not just from my experience as a child and parent, but also as a teacher in schools with high mobility rates- I have seen children experience moves both ways and it has always been smoother when the children know in advance. Involving the children early also means you don't have to try to take care of logistics or deal with your own stress in secrecy, which will in turn reduce your own stress. As soon as I found a house that I liked and decided to pursue it, I started saying things to my girls like, "you know, someday soon it might be good to move to a bigger house. You girls are getting so big!". Once I had the house under contract, we went to look at the house together. Once I had a tentative move-in date, I put it on their calendar and started talking about it often. When I almost didn't get to move in because of stalled paperwork, I told the girls that the workers were helping me buy the house, but it might take longer than I thought- we just had to wait and see. Thankfully we did get to move in on our scheduled date, but I felt confident that they understood the situation either way, and the it was worth the uncertainty to have them be prepared for the big change.
2. Talk to them about the good and the bad
Depending on the situation, you as a parent may have very strong feelings one way or the other about moving. Your children will, in most cases, have mixed feelings. No matter how much you hate your old house, or hate the thought of moving, dig deep and find that small part of you that can appreciate something about your old place, or look forward to the new place. Talk to your kids about the specific things you love about your current house, and the specific things you are looking forward to in the new one, and encourage them to do the same. They shouldn't feel guilty for loving their current house and feeling sad to leave it, or about being excited about the new possibilities in the new house. Again, the earlier you can start those conversations with your children, the more time it will give them to work through their mixed feelings and find ways to express them in a healthy way. The most wonderful words I have ever heard my change-resistant daughter say were when she very matter-of-factly announced that she was "sad to leave her old house, because it is our house, but excited about our new house, because it has a yard"!
3. Have them help with packing
It's always easier to pack without the kids there. I won't lie and tell you that I involved my girls in the entire packing and moving process- I picked my move date specifically because the girls were going to be away visiting their dad for the day! But I did have the girls pack a few boxes of their own toys and clothes, and I think it helped them realize what was happening and feel a part of the process, and less like the move was being forced on them against their will. We wrote their names on their boxes and decided together where those things should go in the new house. As a child I remember the painful process of choosing which toys to keep and which to give or throw away. If your packing space is limited, make sure your children make the final decisions on what stays and what goes, and let them be involved in giving or throwing away so they can "say goodbye" to their belongings as well.
4. Help them say goodbye
For us, the only thing we were really saying goodbye to was our apartment- we still have the same neighborhood, same school, same friends. So for my girls, saying goodbye meant going to the apartment after it was empty and saying goodbye to each room. For me as a child, moving often meant saying goodbye to friends, school, neighborhood, even language and culture. It's important to help your children think through all of the things that they are leaving and helping them to say goodbye to each of them. This is also a great time to help your children say thank you to important people in their lives- teachers, friends, and others who won't be around after the move. If they are old enough, cards are a great way for children to say goodbye and thank you in a concrete way.