When you select (Back Office >> Shipping >> Countries) you will see what countries in your Prestashop installation are allocated to what zones.
In addition, this is where you set the default country for your shop, so if you are in the UK, select United Kingdon.

You can choose to edit an existing country, delete a country or create a new country.
In this example we will add a new country. Click "Add New" (editng a country will present the same screen options however as shown below)

Country Name: Enter the Country Name for the current language (click the flags to enter country descriptions in that language - this needs checking!)
ISO Code: Enter the correct ISO code for the country. Offical IS0 3166-1 County Codes
Zone: Choose the correct zone from the drop down list. (Your zones must be created before setting up countries)
Status: This your zone enabled or disabled. If disabled it will not be shown in the frontoffice and no shipping charges to this country will be applied by Prestashop.
Contains States: Does this coutry have states, Y or N (Note, for USA you do not need to create a country, you only need the zone to be created. When you choose states from the sub-menu, the zone USA can be applied to each state but there is no option to select any other country other than USA)
Once you are happy with your entry, select save.