It is very simple. Creat a profile for your website in twitter, and then paste twitter button on your website. It is in code shape. You can easily understand from code where you have to put your twitter url of website. For more info please go to page net.tutsplus.com/articles/10-awesome-ways-to-integrate-twitter-with-your-website
I got a lot of information on this page smashingmagazine.com/2009/03/02/twitter-web-designer-and-developer-toolbox-api-and-tutorials/ I have removed http://www. from the url