If you're just getting started with wanting to integrate Twitter into your site, than simply adding the traditional Twitter widget to your site's sidebar is a great start. It's not sexy, but it's a great way to show your latest tweets on your website. It's an effective way to get readers involved into your Twitter updates, without taking up too much screen real estate.
Twitter widgets can be used with virtually any site or blog, including HTMl-only pages. While they may not require the most exciting development hack to incorporate Twitter into a website (copy + paste), simplicity is not a bad thing.