Analyse the requirements. Understand what the api should do. Check which data is needed. Choose a point where the api should be integrated.
Develop an architecture, choose which technologies should be used. Determine the timeline for the integration.
Test the endpoints and implement them. Do the same for the integration.
Make sure you avoid the common fallacies of distributed computing:
This could be a good starting point for your test cases. The term "distributed" can be applied in terms of time, space and hierarchy - over time the network may change, the distribution may cover large areas and incorporate multiple levels of hierarchy.