1. Edit the config section in twitter_badge.php
2. Include the file into your code like this:

<div id="twitter-box">
	<h2>Twitter</h2>
	<ul id="twitter-updates"><?php include 'twitter_badge.php'; ?></ul>
</div>

3. Or since contacting Twitter may increase your site load time, use:

<div id="twitter-box">
	<h2>Twitter</h2>
	<ul id="twitter-updates">Loading tweets...</ul>
</div>

with the following Javascript (note, this code is for jQuery; you can adjust accordingly to standard Javascript or any other framework):

$(document).ready(function(){
	$("#twitter-updates").load("twitter_badge.php");
});

4. Style #twitter-box, #twitter-updates, and #twitter-updates li however you like (you can even change the ID/classes if you would like too).