Since there is no real question asked here, I Will give an answer that seems suiting to your problem.
First you need to use Asyntasks, then after you treated the response you should do something like getting the instance of your database and calling the right Insertion method by passing it your the JSONObject. If it's a JSONArray, then you should loop on the array calling that function (passing the object you're on in the loop).
You could also have an object that will parse your JSON into itself, then you could call the insert methode which suits to the object.