How do I access the HTTP request header fields via JavaScript?

Almost by definition, the client-side JavaScript is not at the receiving end of a http request, so it has no headers to read. Most commonly, your JavaScript is the result of an http response. If you are trying to get the values of the http request that generated your response, you'll have to write server side code to embed those values in the JavaScript you produce.

It gets a little tricky to have server-side code generate client side code, so be sure that is what you need. For instance, if you want the User-agent information, you might find it sufficient to get the various values that JavaScript provides for browser detection. Start with navigator.appName and navigator.appVersion.

If you want to access referrer and user-agent, those are available to client-side Javascript, but not by accessing the headers directly.

To retrieve the referrer, use document.referrer.
To access the user-agent, use navigator.userAgent.

As others have indicated, the HTTP headers are not available, but you specifically asked about the referer and user-agent, which are available via Javascript.

This can be accessed through Javascript because it's a property of the loaded document, not of its parent.

Here's a quick example:

<script type="text/javascript">
document.write(document.referrer);
</script>

The same thing in PHP would be:

<?php echo $_SERVER["HTTP_REFERER"]; ?>