Facebook OAuth 2.0 Credit: http://thinkdiff.net/facebook/new-javascript-sdk-oauth-2-0-based-fbconnect-tutorial/

functions.js

window.fbAsyncInit = function() {
  FB.init({ 
		appId: 'Your_APP_ID',
		status: true,
		cookie: true,
		xfbml: true,
		oauth: true
	});

	showLoader(true);

	function updateButton(response) {
		button       =   document.getElementById('fb-auth');
		userInfo     =   document.getElementById('user-info');

		if (response.authResponse) {
			//user is already logged in and connected
			FB.api('/me', function(info) {
				login(response, info);
			});

			button.onclick = function() {
				FB.logout(function(response) {
				logout(response);
				});
			};
		} else {
			//user is not connected to your app or logged out
			button.innerHTML = 'Login';
			button.onclick = function() {
				showLoader(true);
				FB.login(function(response) {
				if (response.authResponse) {
						FB.api('/me', function(info) {
						login(response, info);
					});
					} else {
						//user cancelled login or did not grant authorization
						showLoader(false);
					}
				}, {scope:'email,user_birthday,status_update,publish_stream,user_about_me'});
			}
		}
	}

	// run once with current status and whenever the status changes
	FB.getLoginStatus(updateButton);
	FB.Event.subscribe('auth.statusChange', updateButton);
};
(function() {
	var e = document.createElement('script'); e.async = true;
	e.src = document.location.protocol
	+ '//connect.facebook.net/en_US/all.js';
	document.getElementById('fb-root').appendChild(e);
}());

function login(response, info){
	if (response.authResponse) {
		var accessToken                                =   response.authResponse.accessToken;

		userInfo.innerHTML                             = '<img src="https://graph.facebook.com/' + info.id + '/picture">' + info.name
		+ "<br /> Your Access Token: " + accessToken;
		button.innerHTML                               = 'Logout';
		showLoader(false);
		document.getElementById('other').style.display = "block";
	}
}

function logout(response){
	userInfo.innerHTML                             =   "";
	document.getElementById('debug').innerHTML     =   "";
	document.getElementById('other').style.display =   "none";
	showLoader(false);
}

function streamPublish(name, description, hrefTitle, hrefLink, userPrompt){
	showLoader(true);
	FB.ui({
		method: 'stream.publish',
		message: '',
		attachment: {
			name: name,
			caption: '',
			description: (description),
			href: hrefLink
		},
		action_links: [
			{ text: hrefTitle, href: hrefLink }
		],
		user_prompt_message: userPrompt
	},
	function(response) {
		showLoader(false);
	});
}

function share(){
	showLoader(true);
	var share = {
		method: 'stream.share',
		u: 'http://thinkdiff.net/'
	};

	FB.ui(share, function(response) {
		showLoader(false);
		console.log(response);
	});
}

function showStream(){
	FB.api('/me', function(response) {
		//console.log(response.id);
		streamPublish(response.name, 'I like the articles of Thinkdiff.net', 'hrefTitle', 'http://thinkdiff.net', "Share thinkdiff.net");
	});
}

function graphStreamPublish(){
	showLoader(true);

	FB.api('/me/feed', 'post',{
		message     : "I love thinkdiff.net for facebook app development tutorials",
		link        : 'http://ithinkdiff.net',
		picture     : 'http://thinkdiff.net/iphone/lucky7_ios.jpg',
		name        : 'iOS Apps & Games',
		description : 'Checkout iOS apps and games from iThinkdiff.net. I found some of them are just awesome!'
	},
	function(response) {
		showLoader(false);

		if (!response || response.error) {
			alert('Error occured');
		} else {
			alert('Post ID: ' + response.id);
		}
	});
}

function fqlQuery(){
	showLoader(true);

	FB.api('/me', function(response) {
		showLoader(false);

		//http://developers.facebook.com/docs/reference/fql/user/
		var query       =  FB.Data.query('select name, profile_url, sex, pic_small from user where uid={0}', response.id);
		query.wait(function(rows) {
			document.getElementById('debug').innerHTML =
			'FQL Information: '+  "<br />" +
			'Your name: '      +  rows[0].name                                                            + "<br />" +
			'Your Sex: '       +  (rows[0].sex!= undefined ? rows[0].sex : "")                            + "<br />" +
			'Your Profile: '   +  "<a href='" + rows[0].profile_url + "'>" + rows[0].profile_url + "</a>" + "<br />" +
			'<img src="'       +  rows[0].pic_small + '" alt="" />' + "<br />";
		});
	});
}

function setStatus(){
	showLoader(true);

	status1 = document.getElementById('status').value;
	FB.api({
		method: 'status.set',
		status: status1
	},
	function(response) {
		if (response == 0){
			alert('Your facebook status not updated. Give Status Update Permission.');
		}
		else{
			alert('Your facebook status updated');
		}
		showLoader(false);
	});
}

index.php

<!DOCTYPE html>
<html xmlns:fb="https://www.facebook.com/2008/fbml">
</html>