The good news is that your markup is somewhat correct. So is your CSS but it's just not complete.
You do need to fix your DocType and other errors. First off, I would suggest that any new site should have a Strict DocType, not a transitional. Have a look at the link in my signature about DocTypes.
You style the ul#nav, it's li's and the anchors in those li's but you don't style the dropped ul. You need CSS that hides the dropped ul until it's parent li is hovered. Then you need to style how you want that ul and it's li's to look.