Moving is painful, logistically as well as emotionally. Here are some things I've learned from my recent experience:
(1) Make a plan as soon as you know you're moving. If possible - timeline backwards. Moving on this date, when will packing be done? Do you need to make a trip to the new location to apartment hunt? Count on packing taking longer than you think. What services do you think you'll need? Cleaners, movers, carpet shampooing, etc. etc. Start emailing your friends for referrals.
(2) List companies/addresses that will need your new mailing address. This is easiest if you start a few months before your move: utilities, banks, investments, magazines, Sallie Mae, etc. etc. As your mail comes in, add addresses to the list. Having it all in one place will kick much ass later.
(3) Go through your crap. If you've lived in one place for a while, this will be especially sucky. I divided it up by doing one area each weekend (one closet, one bookshelf, etc. etc.) Triage into throw away, give away, and take with you. Goodwill will pick up, if you have enough stuff and you schedule sufficiently early. Look into other local charities that accept donations. Check out animal shelters - they often need shoeboxes, as well as towels, linens, etc. Many charitable organizations dealing with domestic violence take cell phones. Also, look for charities that accept business clothing, for example Dress for Success.
Here's where the emotional stuff tends to kick in. Remember that everything you are going through is perfectly normal. Try writing, or bitching to friends (even though you will be worried about wearing our your welcome, in that regard.) Take time for yourself as much as possible. Keep a countdown - it is at once a source of stress, and relief.
(4) Collect packing materials. You can often get packing materials from friends, or off of Craigslist. Boxes, packing tape, scissors, newspaper, markers. Keep the things you'll need right away at your new location apart - shower curtain, trash bags, cleaning materials, toilet paper, a towel, etc. Not being able to take a shower after moving - not cool.
(5) Contact the post office and others on your list from #2. You can even change your address with the USPS online. Some subscriptions etc. take 6 weeks to change your address, so get in touch as soon as you know your new address.
(6) Pack. This is a good time to do more triage. Mark each box with the room it came from, and the contents. If you're really geeky - color code.
(7) Cleaning Or: how to get your security deposit back. Consider hiring cleaners. If the budget won't allow, use your bucket of cleaning materials and hop to it. For white walls, you can use (white) toothpaste to fill in the holes where you hung your artwork collection. For carpets, use ammonia and a brush with plastic bristles (dollar store, baby) to get up the worst of the stains. Rent a carpet cleaner (I got mine from my grocery store) and use Oxiclean detergent in it (skip the expensive stuff they try to sell you at the store.) (For both the ammonia and the rug cleaning, test an inconspicuous spot first.) Take pictures of the place when you're done.
(8) Unpacking. Thankfully, this process is about 5 times faster than packing. Stop at the grocery store for snacks and a flat of water. Make sure your new place is as clean as you'd like. Move boxes into the rooms they have been marked for. Use your "set aside" box to to set up your shower (trust me, you'll need it.) Do as much unpacking as you can the first day, because otherwise the task can suddenly stretch on for days/weeks/indefinitely (we still have packing boxes in our basement from when we moved from Geneva - i.e. when I was 7.)
(9) Pizza and beer. Hey - it's a moving tradition!
If you have enough time, consider holding a garage sale to get rid of some of your stuff (maybe pool together with other friends who are also moving/looking to scale back.) Another option: use Craigslist or EBay to make some $$ off your unwanted stuff.