1. Don't do it. If you can avoid moving during those testy years, do it. But if you must move, go on to tip#2.
2. Put packed boxes in a safe place. We all know that toddlers love to explore things that are unfamiliar to them. Boxes stacked all over the house that are waiting to be taken to their new destination are like candy. They are just irresistible to a toddler. No matter how many times your tell them to leave the boxes alone, they will get into them over and over again. Do yourself a favor and find a safe spot to store them. In our other apartment, there were storage units in the hallway. We were able to use one of the empty storage spaces during the month we moved. This kept a lot of the clutter associated with packing out of our house and out of Nate's curious hands. Maybe you have a garage you can put your boxes in. Or maybe there is a bedroom that your toddler doesn't go into where you can store them.
3. Get your husband some help on moving day. When the boxes are being loaded into the moving truck and taken to the new house, someone, most likely you, will need to stay with the toddler. Either enlist a family member or friend to take care of your child so you can help with the loading, get some guys to help your husband out, or splurge a bit on hiring some movers. In my opinion, getting some movers to help out relieves a lot of the stress accompanied with moving day.
4. Designate a "safe spot" for your toddler while boxes are being moved and unpacked. This could be a bedroom free of boxes where your child can play. In my case, it was a Pack-n-Play. As much as I hate confining Nate to a play pen for too long, it was nice being able to put him in a safe spot and know he wasn't getting into any trouble.
5. Unpack everything as quickly as possible. Even if it means staying up a few hours past your bedtime, do it. At the very least, make a safe area that can be gated off for your child to play. This will save you a lot of stress while you do the rest of the unpacking.
If you do these things, your move should be easy-peasy. Well...easier than it would be if you didn't do these things. :)