Use the right boxes
You'll need many boxes in assorted sizes. All boxes should be in good condition, and must have covers on them in order that they can be closed up and sealed. You can
purchase cartons from your mover, a store, or online. Don't expect your mover to
provide them for free.
You might start collecting cartons from your local grocery and liquor stores. All too
often grocery store cartons have the tops removed, but if you have a talk with the store manager he/she  would probably be willing to save you some cartons with the covers still intact. Liquor cartons are excellent packing cartons. They are sturdy, and contain dividers which make them ideal for packing glasses, goblets, vases, etc.

Pack carefully
It is imperative for you to buffer and separate fragile objects with sheets, blankets,
pillows and towels. Fill in empty spaces to minimize movement during transit. Pack plates and glass objects vertically, rather than flat and stacked.
Be sure to point out to your mover the boxes in which you've packed fragile items,
especially if those items are valuable. The mover will advise you on whether those
valuables need to be repacked in sturdier, more appropriate boxes.  If you have any
sentimental, or expensive items that you do not want harmed take them with you.  Better to be safe than sorry.

Facilitate the transit
The heavier the item, the smaller the box it should occupy. Label all boxes so you can find everything you need the first night in your new home. You should also label each box to show which room they belong to.  When you are unpacking at your new home show the movers where each room is so they can put the boxes in the appropriate
location.

Safety
Teach your children your new address and phone number before you move. Let them practice writing it on packed cartons. 

"Essential" boxes
These boxes will consist of the essential items your family will undoubtedly need for
the first night. Fill two cartons with snacks, instant coffee/tea bags, medicine, towels, various toiletry items such as toothbrushes, toothpaste, soap, and toilet paper. Other
essential items include flashlights, can openers, paper plates and cups, plastic utensils, screwdrivers, scissors and pliers. Why the second box? It will serve as insurance in the event that your movers experience delay getting to your house.

Don't forget about what you need the next morning.  Coffee drinkers make sure you have a coffee pot, beans, filter, etc.  Also include a change of clothes for your whole family.  A good idea is to pack a bag like you are going on vacation for a few days.  This will give you time to find everything you "lost" in the move.