Make a list.
Write everything down! You'll thank yourself later. Before you pack even one box, create a simple record keeping system. Create a computer-printed list of numbers with a space to write out the contents, or have a spiral-bound notebook for the job. You'll place a number on EVERY box you pack and list the contents on your list. Don't put the list down unless it's in a place you'll call "packing central". This is where you'll find your labels, marking pens, box tape, and other supplies. When describing the box contents, be specific "A-D files" is better than "files", and "Tulip dishes" rather than "misc. kitchen".
Have plenty of supplies.
Don't make me say this twice-- you'll need LOTS of boxes probably more boxes than you think, and having enough boxes will make your life easier! (If you buy your boxes from a moving company, you can always return unused boxes for a refund. If you got them free from the grocery store, just toss out any leftovers). Have about 10 boxes set aside to use for last minute items on moving day, such as bedding, clothing, and cleaning supplies. You'll need strong plastic packing tape to close up the boxes securely. Use unprinted newsprint (newspaper can stain your items) or packing paper or bubble wrap to wrap and cushion household good. Again, you'll need lots more supplies than you think, so get extra to ensure that packing can go smoothly. Return any unused supplies after the truck is packed.
Keep things together.
Insist on keeping things together when you or the movers are packing boxes. Keep bookends with books, light bulbs with lamps, and extension cords with appliances. Small, loose parts can be attached to the item they belong to with tape or placed in small envelopes -- to keep picture hooks with pictures, shelf brackets with a bookcase, a special wrench and bolts with the wall unit. Keep larger corresponding items (such as a cable TV cord) in resealable bags, and tape these to the underside or back of the item. As a backup, have a "Parts Box" open on the kitchen counter and fill it with cables, cords, parts, pieces, brackets, or nails that are removed from any items of furniture. Keep this box with you, or mark it well with a rainbow of colored stickers so it can be easily located on move-in day.
Anything you can pack ahead will save you time on moving day. If it's summer, get your winter clothes out of the way. You don't really need 5 radios or tvs around your house for the last few days there. Box up your shampoo and extra toothpaste and live out of a travel cosmetic case for the last week or two. Pare down cooking utensils and food supplies to bare essentials. Wastebaskets can also be packed (put things in them!) while you switch to using plastic grocery bags (hang them on a cabinet door, or door handle to collect trash).