Facebook is everywhere and almost everyone got a facebook account. As you can see on lots of major site they have implemented facebook in to their website so people can share their information on facebook.
Get Started by first going on this link:
http://developers.facebook.com/docs/reference/plugins/like
(may sure you already login to your facebook account)
There is a form on this page that you'll use to setup your like button.
First, enter the address of your site. If you leave this field blank, people who click your like button may end up liking something else entirely.
It is recommended that you should enter your Facebook Fan Page address and prefer visitors Like that page but if you enter your Weebly website address they will just end up Liking your site and it will not increase your Likes on your Fan page. The (Web-Support) Facebook Fan page is located at http://www.facebook.com/pages/Web-Support/298717333518827, so if i wanted visitors to become my fan Fans, I'd enter that address in the box instead of entering the
www.web-support.weebly.com address.
Make sure the Send Button option is turned off / unchecked. This is a new option from Facebook that Weebly don't currently support.
Then select your layout style. This will change the example layout shown to the right of the form.
Decide whether or not you want to show the faces (profile pic thumbnails) of some of the people who've liked your site. The design usually looks cleaner if you uncheck this box.
Set the width of the like button and description. This defaults to 450 with the standard design (which would work just fine with most sites) but I'll suggest you should use 400 width maximum only for weebly sites you may want to make it narrower if you're placing this in a 2-column layout or sidebar.
Choose a button that says Like or Recommend, which font you want to use and a light or dark color scheme. Then click the Get Code button to see the code you'll be adding to your site.
once you're able to click the "Get Code" button, you'll be presented with a dialog box.
Select the iframe code and copy it. This is important as the XFBML code will not work properly.
After that Open your site in the Weebly editor, drag and drop the Csutom HTML Box element to a page where you want to place you facebook LIKE button and then paste the code there.
Finally Publish your Website! your site is live now and you are done.
You can use this same button code on as many pages as you want. That way visitors can like your site no matter which page they're on.