The easiest way to do this is to use the protected Json method on the Controller class. This will take an object and return it's JSON representation using in a JsonResult.
Using your example:
public ActionResult GetPinPoints() {
return Json(jsonobject);
}
If you do not like the way that ASP.NET MVC serializes your object into JSON, you can do it yourself, creating an ActionResult which will take your object (or the JSON you build) and write the contents back to the response stream. Just make sure that the ContentType that you send back is of type application/json or text/javascript.
From there, you can use a call to getJSON in jQuery to get the results and then use the object however you wish.
Note that if you don't need anything overly complex, or your designs don't call for it, you do not need the HttpPostAttribute.