As mentioned earlier, you use JavaScript to do this.
But the user of your site may get a warning message:

This will copy the contents of the clipboard to the clipboard if you click in the textarea with the mouse.
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "
http://www.w3.org/TR/html4/strict.dtd">
<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>Copy To Clipbord</title>
<script type="text/javascript">
<!--
function copyFieldToClipboard(objEl) {
objEl.select();
window.clipboardData.setData("Text", objEl.value);
alert('Copied data to clipboard');
}
//-->
</script>
</head>
<body>
<textarea name="click_to_copy" rows="10" cols="60" onclick="copyFieldToClipboard(this)">Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Cras dolor. Sed sed neque. Duis eros justo, bibendum in, placerat eget, ullamcorper vel, nibh. Praesent urna arcu, sagittis eget, semper laoreet, tempus non, augue. In a pede. Vestibulum consequat eleifend sem. Duis tristique tortor ultricies massa. Duis sapien eros, posuere sit amet, rhoncus non, venenatis bibendum, tellus. Donec dui tortor, dignissim quis, eleifend eget, fermentum a, massa. Maecenas vel enim vitae sapien condimentum eleifend. Duis hendrerit luctus dui. Donec sem dui, posuere a, consectetuer eget, pretium aliquet, turpis. Vestibulum posuere porta lacus. Sed convallis molestie purus. In hac habitasse platea dictumst.</textarea>
</body>
</html>