As is being discussed in Itay Moav's answer, writing to a local file with a local HTML file is perhaps going to be an issue without running in an elevated privilege mode and having additional Javascript capabilities (that allow you to save local files).

However, accessing a local file from an HTML file is entirely possible. Below is some example code.

mytext.txt

My local text file

local.html

<html>

<head>

<base href=file:///C:/path/to/your/folder//>

<script>

window.onload = function(){

    var iframe = document.createElement('iframe');

    iframe.id = 'iframe';

    iframe.style.display = 'none';

    document.body.appendChild(iframe);

    iframe.src = 'mytext.txt';

    setTimeout(function(){

        var text = document.getElementById('iframe').contentDocument.body.firstChild.innerHTML;

        alert(text);

    }, 1000);

}

</script>

</head>

<body>

<h1>Hello World!</h1>

</body>

</html>

This will make an alert 1 second after the html page loads (to allow the iframe to load first), and will contain the content within the mytext.txt file.

Note, if it's plaintext, Firefox will wrap it with a PRE element, which is why I did firstChild. Also, note the use of the BASE element, which points to your local directory with your files.