This will get you started with cookies.
ASP.NET Cookies Overview[
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You could present them with a drop-down containing a list of countries and ask them to select. Once selected create a cookie. Next time in attempt to read the cookie. If it's there don't display the drop-down since you know where they are from otherwise start again.
Note that you might be better to persist this information in a database as cookies do get deleted or are not always allowed.