Let's start with backend. Assuming an object has been posted to the extension, here's how you retrieve it in your function:
var ff = require('ffef/FatFractal'); // FatFractal module
var data = ff.getExtensionRequestData(); // Get request data
var member = data.httpContent.member // Get 'obj' member of passed object
Alright, so now you've done some stuff and want to return something, here's how you do that:
var r = ff.response(); // Get response object, and populate
r.result = { member: "Something", otherMember: false, yaMember: 42 };
r.responseCode = "200";
r.statusMessage = "This message is useful";
r.mimeType = "application/json";
Finally, to the client side. Here's how to post an object to the extension:
var ff = new FatFractal();
// ...
ff.postObjToExtension({ member: "derp" }, "/yourExtension", ... );
Hope that clarifies things!