You don't need to create adapters and handlers. IN the article Alan wrote he explains how the handlers and adapters work. But they are already there. Of course if you want to add a new type of service you may need a handler but Magento already has SOAP and REST. What more do you want? :).  

Here is a small example on how you can [extend the existing API][1]   
Here is a big example on how you can [add the files needed for the API][2] in your custom module.  

I can also recommend you [this extension][3]. It will build you a module with the SOAP API files included. It could be a good place to start learning how it works.  
Build a module with it with the API included and one without the API then see what are the differences. that will tell you what files you need to create for the API.


  [1]: http://magento.stackexchange.com/a/1331/146
  [2]: http://magento.stackexchange.com/a/9502/146
  [3]: https://github.com/tzyganu/moduleCreator