The bare minimum JavaScript code needed to get a Facebook app up and running with an authorization prompt. User token is saved to a cookie for retrieval by server side code.

myfacebookapp.js

/*
complete facebook sdk authorization/login in 20 lines (or less)
include https://connect.facebook.net/en_US/sdk.js in your html page
*/

function onLogin(response) {
    if(response.status === "not_authorized") {
        // send the user somewhere as they refused to authorize your app
    }
}

function onStatusChange(response) {
    if(response.status === "not_authorized") {
        FB.login(onLogin);
    }
}

$(document).ready(function () {
    FB.init({
        appId: 'YOUR_APP_ID',
        cookie: true, // save a cookie for the session so we can get it on the server side
        status: true, // retrieve the status on each page load so we don't have to call getLoginStatus ourselves
        version: 'v2.4'
    });
    FB.Event.subscribe('auth.statusChange', onStatusChange);
});