You can accomplish this with jquery.
Place this code in index.html
<html>
<head>
<title></title>
<script src="//code.jquery.com/jquery-1.10.2.js"></script>
<script>
$(function(){
$("#footer").load("footer.html");
});
</script>
</head>
<body>
<div id="footer"></div>
</body>
</html
Here is a stack overflow page that can help you with this
Also if you are using php this will be more simple
<html>
<body>
<h1>Welcome to my home page!</h1>
<p>Some text.</p>
<p>Some more text.</p>
<?php include 'footer.php';?>
</body>
</html>
Just create your footer in footer.php
Here is w3schools post if you want to know more about php and how to include this.