The first step in setting up shipping charges for your cart is to determine how you would like to charge for shipping and the amounts to use. Is your shipping based on weight, or number of items? In addition to the zip code what other factors are used to determine how much to charge for shipping?
Once you have this criteria clearly defined you can then go about creating your shipping charge rule. If you can post back with this information and an example scenario and how much it should cost for shipping I can help to give you some pointers on what you will need to do to get the rules in place.