It's not likely that you'll have to file a claim, but if you do, make sure that any losses or damages have been clearly noted on your van operator's inventory sheet before you sign it. (Another reminder: Be sure to safeguard your copy of all paperwork for future reference. Also, if you have items of unusual nature or value, have them professionally appraised before your move.)
Claim forms can be obtained from your movers. These forms provide explicit instructions; however, don't hesitate to call your mover's head office if you have any questions.
It's not necessary to unpack every box immediately, but do look for obvious damage to carton exteriors. Also, for your protection, maintain damaged items in their shipping boxes and do not dispose of any broken or chipped pieces until after your claim has been settled.