Once you've committed to using Twitter to its fullest advantage, you can now start to make it work for your blog. The first thing to do is be sure you have filled out your Twitter profile completely. Put your blog URL in the Website section, talk about what you do at your site in the Bio, and also put your city, or the nearest recognizable city to you, in the Location section. Many people don't like to give out their location to online sites, however with Twitter it will only be a benefit - there are lots of local Twitter gatherings in cities around the world that offer expanded networking opportunities.
Use your tweets as a platform to get the word out about your blog posts and website promotions. A common form for a tweet regarding a new blog post is: Blogged This: "Post Title" www.yoururlhere.com. You will be surprised how many of your followers will actually go to the site, especially if you place a "comments would be v. appreciated!" in the tweet as well.
Yet success on Twitter will not come from tweets regarding your blog happenings alone - it is very important to interact with the community, search and follow other people, and engage in dialogs that have nothing to do with your marketing aims. Post a few tweets a week about what you're doing that day, how you are feeling, what time you woke up, what your cat did to your pillowcase, etc. Be sure to reply to other member's posts, click on some of their links, and strike up conversations with them. If you see something on their profile you like, then send them a tweet saying so!
What you don't want to happen: Every time you post, people scan right over it because they know you are just advertising your own stuff - this happens, don' t be one of these members!
What you do want to happen: Every time you put up a tweet your followers read it, and some acknowledge it, respond, or visit your link.
With a little effort, a few minutes a day, and a willingness to give your followers some of your time, you will see increased traffic to your site, gain increased exposure, and may even see other members posting about your blog posts with links to your site - which is how you grow your blog on Twitter!