How to develop a new market to extend your business nationally or internationally?

My advise would be to develop a new market by penetrating through an existing market. What I simply mean is to identify sub segments within your segmented target audience and twist your product or service slightly to appeal to them. I will give examples of companies in both goods and service industries who have done this and were successful.

Goods --> Coca Cola --> Diet coke for diabetes , 200 ml for kids, additional sugar for Mexico market.

Service --> Vodacom --> Area code +44 for High value customers in Qatar, or university bundles for the youth in Tanzania.

I believe they are a number of approaches to the above problem but this is my take. Hope it helps.