Well the best way to advertise your site using twitter is if you follow a lot of people that have an interest in your type of site. For example, if you are a financial site and you know the twitter name of a well known financial site you should follow the people that follow that site and the chances are they will follow back (to make the mass following quick use tweepi). And for you generate traffic to your site post aprox 3 posts every day linking to diferent pages in your site. When tweeping you site pages you should write a sentence about the page you link and because you can only use 140 charachters per post you should use a site like bit.ly to shorten your url addresses and plus they can track the click rate for you!
Good luck with your site!