Capturing the "scroll down" event?

A better way is to not only check for scroll events but also for direction scrolling like below;

$(window).bind('mousewheel', function(event) {
if (event.originalEvent.wheelDelta >= 0) {
    console.log('Scroll up');
}
else {
    console.log('Scroll down');
}
});

Just for completeness, there's another solution using another JS framework (Mootools)

window.addEvent('scroll',function(e) {
    //do stuff
});

If you don't want to use jQuery (which you might not do for a very simple HTML page), you can accomplish this using regular Javascript:

<script>
function scrollFunction() {
    // do your stuff here;
}

window.onscroll = scrollFunction;
</script>

You mentioned that you wanted to do something when they scroll down the page - the onscroll event fires off scrolling in any direction, in either the x- or y-axis, so your function will be called any time they scroll.

If you really want it to only run your code when they scrolled down the page, you'd need to preserve the previous scroll position to compare against whenever onscroll gets called.