That depends entirely on how those calls are being made. Two of the more popular methods today are REST and Webservices. You can use tools like Postman, or a framework like Ruby Airborn to test these. As for test design, the test ideas will be similar to how you test data through a user interface. The only difference is you are using a tool to interface with bits of code rather than a finished user interface in a web browser.
how to test backend server calls?
i am a manual mobile app tester.