In an action (at the controller), you can just do:

ac.done(data, 'json');

That will stringify the data structure, and add the proper headers.

If you want to do it manually, by executing an actual view for example. You can do this:

ac.http.addHeader('Content-Type', 'application/json; charset="utf-8"');
ac.done(data, {
    view: {
       name: 'api-json-view-whatever'
    }
});

So, the result of the done call (will be a string), and it will be sent to the client side as "application/json".

Or maybe a jsonp response:

ac.http.addHeader('Content-Type', 'application/javascript; charset="utf-8"');
ac.done(cb+'('+JSON.stringify(data)+')');

For the second case when I specify the view name. What would be the best approach to implement the view? Should I do it using the moustache template framework? What would be the convention on the file name? 

By default, you can just use a regular mojito view (which is a mustache template). More info here:

http://developer.yahoo.com/cocktails/mojito/docs/code_exs/simple_view_template.html

Put the view as:
<myMojit>/views/<name-of-the-action.mu.html

Best regards,
Caridy

To access any REST Service.. You can use Mojito REST Api given here..
http://developer.yahoo.com/cocktails/mojito/docs/api_overview/mojito_rest_lib.html