I am doing basic http auth with the HttpURLConnection object in Java.
URL urlUse = new URL(url);
HttpURLConnection conn = null;
The JSON string will just be the body of the response you get back from the URL you have called. So add this code
...
BufferedReader in = new BufferedReader(new InputStreamReader(
conn.getInputStream()));
String inputLine;
while ((inputLine = in.readLine()) != null)
System.out.println(inputLine);
in.close();
That will allow you to see the JSON being returned to the console. The only missing piece you then have is using a JSON library to read that data and provide you with a Java representation.
Here's an example using JSON-LIB