Step 1: Get yourself organized. Know where things are going to go in the new place.
Step 2: Start packing everything you don't use on a regular basis. (Books, CDs, DVDs, photos, photo albums, clothes, dishes, pots, pans, towels, sheets, curtains, clothes, etc.). Pack like things together and label the boxes on the front & sides with a number and a letter or color. The letter or color should represent the room the items are designated to while the number represents the number of boxes assigned to this room. EXAMPLE: K-12 of 14 or Red-12 of 14 would let you know this is box 12 belonging to the kitchen and there are 14 boxes belonging to the kitchen. Keep a list of what is in each box. Doesn't need to be anything extensive just a piece of paper you can keep in the box or in a separate note pad. This will help for unpacking.
Step 3: Each person should be assigned a different colored laundry bag for their clothes. This would be a perfect time to give away things that no longer fit or things you just don't want or need any longer or just toss things that can't be given away. This will help when it comes to unpacking too.
Step 4: Put as many things as you can into labeled boxes. You may want to arrange for a sitter if your kids are the kind that get underfoot or really have them help bring their things to the new place.
Step 5: Go through the toys because this will also be a great time to purge and pare down by throwing broken toys out and really giving some toys they don't play with away. This will make the move easier.
Step 6: The last things you want to pack on moving day is the first things you want to unpack meaning each person should have a set of clean sheets, pajamas, curtains, blankets, towels, wash clothes, and one set of dishes to make the first day's meal. This box or boxes should be something you keep track of and don't let anyone else move for you. Each person will need their own first night box. The kids may want to add their favorite toy, lovey, or prized possession to this box.
Step 7: You should pack dishes up with your spare towels, wash clothes, sheets and dish towels. This is killing two birds with one stone.
Step 8: You may want to spend time making certain the new place is clean to your liking before you actually move in. It is easier to clean a cleared out space than it would be when you things get there.
Step 9: See if you can get some friends to help you with your move for an hour or two. This will help the time fly by. The more organized you are the shorter and less stressful your move will be.
Step 10: Your SO will need help moving the large items and you are probably not that help, so get some muscular help too for the heavy things. You may consider renting a hand truck from a rental truck place. They are reasonably priced and will help your move be so much better.
This probably isn't everything but it is a great place to start and really helps take the edge off when moving.