When you give blood or vote, they usually give you a sticker to put on your shirt to proclaim to the world what you just did. "I Voted!" or "I Just Gave Blood!" There should also be stickers that say "I'm Moving Today," so that people can tell at a glance how much stress you're under, and either stay out of your way or randomly give you hugs and cookies, maybe even the occasional spontaneous backrub.
Because moving is stressful. The only things more stressful are divorce or a death in the family. So what can you do to make it less stressful? Well, until you start getting random backrubs from complete strangers on the street (which shouldn't be awkward for anyone), you should try to eliminate every tiny scrap of uncertainty you can from the entire moving process. And that means planning.
The more thought you put into the front-end of your move, the less stressful the move itself will be. Checklists are your friends. Use them for everything you can think of -- cleaning, packing, garage sales, change-of-address forms, moving day meals, utility notifications... You may end up needing a checklist to keep track of all your checklists, but at least you'll be prepared.
Knowing what your move will cost can also save you a lot of stress. You can find a host of moving cost calculators online to ballpark the figure, but moving cost calculators will never tell you the whole story. You can either radically overbudget your moving costs so that you have room to absorb any unexpected costs, or you can have a professional mover come in and assess your belongings with a trained eye.
Finally, consolidate as many tasks as you can, to get more done at once. While you're packing, separate out the things you don't want and then hold a yard sale. While the grownups are clearing closets and stuffing boxes, have the kids do the cleaning. And most moving container services also let their units double as portable storage units, so your items to be stored can be whisked (whisked, I say!) away to the storage facility without you having to shuffle the boxes around.
We don't get stressed about things we know are coming, things we expect -- it's the little things we don't expect, or didn't think of, that tip us over the edge. Even if something is difficult or time-consuming, as long as we know it's coming, we're much more emotionally prepared to deal with it. Things like checklists, moving cost calculators, and portable moving containers can go a long way towards keeping you as Zen as possible during a very un-Zen-like time of your life.