There are two ways you could do it, first off, do you have Gmail, or google sync on your storm. If not you could get both, because you would pretty much need them anyways to use the Droid to it's fullest, and once you get them, you could use google sync to sync your contacts from your storm to your gmail account, then once you get the Droid, the Droid will sync your gmail contacts to your phone.
I'm also sure that if you go to a Verizon store, they can do this for you as well, but I am unsure of how well they sync them over. There were able to do this from my treo to my storm when I bought the storm about a year ago.