At the time itself you should make a small link between your Facebook page and Like Button.Most of us just Google search for Facebook Like button Code and Copy down the Code for Like Button.
Unfortunately it Just give a Like button but never connect with your Facebook Page.
Now,Listen How to connect Like Button and Facebook Page.
Go to Facebook Plugin Page.
Select Like Button from the displayed Plugins

Here You may be redirected into Get Like Button Page (Click Here)
Now Go to Your Facebook Page and Copy the URL of Facebook Page.


Now Go back to Facebook Like button Page , and Paste the URL in the First Text Box Showing URL to Like .Now Just customize the Layout Style,Font,Width according to your convenience.Mark on Face show will show profile Picture and names of your Liked users.
After,Click On the Get code button at Right Bottom.It will popup a Window showing some codes in Iframe and XHTML. Bloggers Must Copy down the Iframe Code and Paste it in your Blogger Sidebar in HTML mode.
Now Save the Code and Refres