I have putting a few blogs about API testing in the past few months. I have been doing some research about how to test API, best tool to test API, etc and I guess there is no exact answer to this. However, SoapUI seems to appear in quite a number of searches. But I still do not choose SoapUI as it is not a pure Open Source tool.
So, I still think it all depends on the language of your API system, and there is a lot of built-in library to make a web request. All you need to do is to incorporate a unit testing framework to assert the result returned.
As I am working in a .NET environment, I have tried HttpClient and WebClient. I have used Curl for Ruby.
Example of POST and GET have been posted in the previous blogs.
Example of PUT is as below: