Add New Region / State
Settings->International Settings->Zones

Overview
You can select a country, and for each country add new regions.
Then for each region you can Add New City.
Then for each city you can set the shipping fees.


Elements
{Select a country}
Select the desired country

{Select a region}
You can select a region and [Delete selected region]


Add new region for United States

Add a new region for the selected country

Add region code
Add a code for the specific region

Links

From here you can:

Select a country {select a country}  
Select a region {select a region}  
Delete the selected region [Delete selected region]  
Add a new region for the selected country [Add new region]