There is no direct integration into Drupal, even from any of the existing API libraries available. To clear up the confusion:

> The API provides you access to the API interface, hosted by Stack Exchange which you can then use to **develop** software against and provides you with readonly access to the content of the Stack Exchange sites.

Since your using Drupal, you will need to create your own Drupal modules that will talk to the API directly. The API is well document [here](http://stackapps.com/questions/1/api-documentation-and-help) and will show you the various ways you can use the API. In example, to retrieve a list of sites from the API you can make a call to the `sites` route on Stack Auth:

`http://stackauth.com/1.1/sites`

This will return you JSON which you can then parse in your code and manage.

This is an extremely brief and simplified overview of what needs to be done to interface with the API, the documentation I linked is much more complete.

It would be helpful if you had a more exact question about using the API however.

Since based on your question, all you want to do is display questions in Drupal, have you considered just using the normal RSS feed from the actual site your interested in, using the existing Drupal RSS modules?