Ok, sorry, thought you were using a different template.
What you need to do is to have classes for your li elements, or an id for your outer ul container, and in your css give them the image as the background.
I presume you want the red dot in front of each main menu item, and the grey dot in front of each submenu item.
<ul id="mainmenu">
<li>item 1</li>
<li">item 2</li>
</ul>
<ul id="submenu">
<li>item 1</li>
<li>item 2</li>
</ul>
Then your CSS would have
#mainmenu li { background:url(images/menudot.gif) no repeat top left; }
#submenu li { background:url(images/submenudot.gif) no repeat top left; }
adjusting the top and left position of the image to get it just right, as well as adding any padding necessary to move the text over to the right so the image shows properly.
There is another option, simply set the list-style-image property of your ul elements. This article is a good source for how to manage list menus...
http://www.alistapart.com/stories/taminglists/