There's some useful information
here.
Be sure to specify that your utilities should be shut off the day AFTER you move out of your old place and turned on the day BEFORE you move into the new place. Utility companies can turn things on/off at any time on the day you specify, and you don't need your electricity or phone going out in the middle of the move.
Label everything and keep a list, especially if you are using movers. Also, don't let them take any valuables, computer equipment, or important/identifying documents.
Get rid of, or use up, any hazardous materials (bleach, propane tanks, etc) and anything perishable - or be prepared to transport them yourself. You will also have to transport live plants yourself.
Make an "unpack me first" box or bag that includes things like box cutters, scissors, tape, cleaning supplies and paper towels, toiletries, snacks, any prescription medications, and a first-aid kit.
Reserve an elevator in both the building you're moving out of and the one you're moving into, if applicable.
Plan out where all your furniture should go in the new place, so you don't end up moving your couch half a dozen times.
Good luck with the move!