You don't need all that code. All you need are the following lines:

<a href="https://www.facebook.com/sharer/sharer.php?u=example.org" target="_blank">
  Share on Facebook
</a>

Documentation can be found at https://developers.facebook.com/docs/reference/plugins/share-links/


You can do this by using asynchronous Javascript SDK provided by facebook

Have a look at the following code

FB Javascript SDK initialization

<div id="fb-root"></div>
<script>
window.fbAsyncInit = function() {
FB.init({appId: 'YOUR APP ID', status: true, cookie: true,
xfbml: true});
};
(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);
}());
</script>

Note: Remember to replace YOUR APP ID with your facebook AppId. If you don't have facebook AppId and you don't know how to create please check this

Add JQuery Library, I would preferred Google Library

<script src="//ajax.googleapis.com/ajax/libs/jquery/1.6.1/jquery.min.js" type="text/javascript"></script>

Add share dialog box (You can customize this dialog box by setting up parameters

<script type="text/javascript">
$(document).ready(function(){
$('#share_button').click(function(e){
e.preventDefault();
FB.ui(
{
method: 'feed',
name: 'This is the content of the "name" field.',
link: 'http://www.groupstudy.in/articlePost.php?id=A_111213073144',
picture: 'http://www.groupstudy.in/img/logo3.jpeg',
caption: 'Top 3 reasons why you should care about your finance',
description: "What happens when you don't take care of your finances? Just look at our country -- you spend irresponsibly, get in debt up to your eyeballs, and stress about how you're going to make ends meet. The difference is that you don't have a glut of taxpayers…",
message: ""
});
});
});
</script>

Now finally add image button

<img src = "share_button.png" id = "share_button">

For more detailed kind of information. please click here


You can read more about share button here on Facebook developers website

Working JSFIDDLE

Also take a look at custom Facebook Share button JSFIDDLE

Include Facebook JavaScript SDK code right after the opening <body> tag

<div id="fb-root"></div>
<script>(function(d, s, id) {
  var js, fjs = d.getElementsByTagName(s)[0];
  if (d.getElementById(id)) return;
  js = d.createElement(s); js.id = id;
  js.src = "//connect.facebook.net/en_US/all.js#xfbml=1";
  fjs.parentNode.insertBefore(js, fjs);
}(document, 'script', 'facebook-jssdk'));</script>

And place below code wherever you want to show Facebook Share button

<div class="fb-share-button" data-href="https://developers.facebook.com/docs/plugins/" data-width="200" data-type="button_count"></div>

enter image description here

Check working JSFIDDLE


For Facebook share with an image without an API and using a # to deep link into a sub page, the trick was to share the image as picture=

The variable mainUrl would be http://yoururl.com/

var d1 = $('.targ .t1').text();
var d2 = $('.targ .t2').text();
var d3 = $('.targ .t3').text();
var d4 = $('.targ .t4').text();
var descript_ = d1 + ' ' + d2 + ' ' + d3 + ' ' + d4;
var descript = encodeURIComponent(descript_);

var imgUrl_ = 'path/to/mypic_'+id+'.jpg';
var imgUrl = mainUrl + encodeURIComponent(imgUrl_);

var shareLink = mainUrl + encodeURIComponent('mypage.html#' + id);

var fbShareLink = shareLink + '&picture=' + imgUrl + '&description=' + descript;
var twShareLink = 'text=' + descript + '&url=' + shareLink;

// facebook
$(".my-btn .facebook").off("tap click").on("tap click",function(){
  var fbpopup = window.open("https://www.facebook.com/sharer/sharer.php?u=" + fbShareLink, "pop", "width=600, height=400, scrollbars=no");
  return false;
});

// twitter
$(".my-btn .twitter").off("tap click").on("tap click",function(){
  var twpopup = window.open("http://twitter.com/intent/tweet?" + twShareLink , "pop", "width=600, height=400, scrollbars=no");
  return false;
});