Here There are 2 Simple Steps
Step 1: Adding Jquery JavaScript Plugin(Ignore this step if your blog have already a Jquery Plugin)
a. Go to Blogger Dashboard < Design tab > Edit Html 
b. Search for </head> tag ( using ctrl+f)
c. Add below line of code Before </head> tag

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

And now click Save Template 

Step 2: Adding Widget Code ( Html code )
it's Simple 
a.Layout or page elements –>> Add a gadget->> Html/java script.
b.Add a below code in the Html/java scipt box.
Replace my facebook page URL below with the URL for your page.
(Note:- Facebook URL Must starting with "http://" and it contains no space or illegal Characters )


<a href="http://24work.blogspot.com" target="_blank" title="Blogger Widgets"><img src="http://safir85.ucoz.com/24work-blogspot/cursor-24work-10.png" border="0" alt="Blogger Widgets" style="position:absolute; top: 0px; right: 0px;" /></a><script type="text/javascript">

//<!--

$(document).ready(function() {$(".w2bslikebox").hover(function() {$(this).stop().animate({right: "0"}, "medium");}, function() {$(this).stop().animate({right: "-250"}, "medium");}, 500);});

//-->

</script>

<style type="text/css">

.w2bslikebox{background: url("http://3.bp.blogspot.com/-YwBHQWHKtfo/Tw2Ewd7XpQI/AAAAAAAAAOc/Nwjd9y_JzjA/s1600/facebookbadge.png") no-repeat scroll left center transparent !important;display: block;float: right;height: 270px;padding: 0 5px 0 46px;width: 245px;z-index: 99999;position:fixed;right:-250px;top:20%;}

.w2bslikebox div{border:none;position:relative;display:block;}

.w2bslikebox span{bottom: 12px;font: 8px "lucida grande",tahoma,verdana,arial,sans-serif;position: absolute;right: 6px;text-align: right;z-index: 99999;}

.w2bslikebox span a{color: #808080;text-decoration:none;}

.w2bslikebox span a:hover{text-decoration:underline;}

</style><div class="w2bslikebox" style=""><div><iframe src="http://www.facebook.com/plugins/likebox.php?href=http://www.facebook.com/pages/Blogspot-tutorial/220888831260608&amp;width=245&amp;colorscheme=light&amp;show_faces=true&amp;connections=9&amp;stream=false&amp;header=false&amp;height=270" scrolling="no" frameborder="0" scrolling="no" style="border: medium none; overflow: hidden; height: 270px; width: 245px;background:#fff;"></iframe><span> / <a href="http://24work.blogspot.com/">+Get This!</a></span></div></div>

</div>


And now click Save