I tried this js code:

<script type="text/javascript">

       $(document).ready( function() {
            var timer;
            $('.top-menu-first-ul li').hover(function(){
                        if(timer) {
                                clearTimeout(timer);
                                timer = null
                        }
                        timer = setTimeout(function() {
                                   $(this).find('ul').slideToggle(100);
                        }, 500)
            },
            // mouse out
            });
        });


</script>

with this html:

<ul class="top-menu-first-ul">
    <li>
        <a href="http://google.com">Google</a>
        <ul class="top-menu-second-ul">
            <li><a href="http://translate.google.com">Google Translate</a></li>
            <li><a href="http://images.google.com">Google Images</a></li>
            <li><a href="http://gmail.google.com">Gmail</a></li>
            <li><a href="http://plus.google.com">Google Plus</a></li>
        </ul>
    </li>
    <li>
        <a href="http://facebook.com">Facebook</a>
    </li>
    <li>
        <a href="http://twitter.com">Twitter</a>
    </li>
</ul>

but it is not working.

I would like to show the submenu when hovering over e.g. Google link and other will appear after 300ms.

So, I need to prevent loading submenu when the user just quickly hover over it and not stay on hover link for at least 300ms.

Then I need to stop executing code (or slide up) when he leaves the link. Because if he go over and back and over and back a copule of times he stop doing hovering anfd the code is still executing itself how many times he had hover over the link. I need somehow prevent this to happen.

EDIT: I need to solve this without plugins like hoverIntent etc. if possible, just plain javascript and jQuery