Hello, 

The key factor you need to check while doing API testing, 

1. callout to external application 
2. authentication and authorization
3. output for your request JSON or XML or other types of data.
4. response trafic.
5. call to other API function, 

here some more other points about  API Testing:
 
Test Cases for API Testing:

 Return value based on input condition: it is relatively easy to test, as input can be defined and results can be authenticated

Does not return anything: When there is no return value, behavior of API on the system to be checked

Trigger some other API/event/interrupt: If output of an API triggers some event or interrupt, then those events and interrupt listeners should be tracked

Update data structure: Updating data structure will have some outcome or effect on the system, and that should be authenticated

Modify certain resources: If API call modifies some resources then it should be validated by accessing respective resources

Approach of API Testing:

Following points helps the user to do API Testing approach:

1.Understanding the functionality of the API program and clearly define the scope of the program

2.Apply testing techniques such as equivalence classes, boundary value analysis and error guessing and write test cases for the API

3.Input Parameters for the API need to be planned and defined appropriately

4.Execute the test cases and compare expected and actual results.

Hope this will clear. 
Mark Best ANSWER fi its clear. 

Thanks
karthik