On the shopping cart screen, you will see a box under 'Discount Codes' that says 'Calculate Delivery'
The customer will have the option to enter the zip code of the recipient here and it will update the charges in the total box accordingly. In following example, we used a zip that was listed in our delivery charges (in your admin go to Settings > Delivery Charge)
This feature will also work for customers who have a recipient outside of your listed delivery zip codes - please use the next example as reference. Note that the delivery charge will reflect your 'Out of Area' delivery charge and 'Wire Out fee' if enabled.