Twitter has really grown up its popularity since its start in March 2006 as a side project in offices in the SoMA in CA. now all around the world; people follow twitter to follow the blogs on their same niche.
To get the best from the twitter you can build a link on your blog and encourage your readers to follow you via twitter. On the other side you can shout about your latest post on twitter. So people who are following you can see you have posted a new one without even accessing your site. You can also update your facebook status from twitter. One thing you must avoid is overloading twitter with linking to every post that you write. It will frustrate your followers and sure they will turn away. I suggest you better pickup 1 post a day and post the link to the twitter. Another thing is posting variety of things. This will not bored your followers and you can come across more and more followers.
If you are beginner to twitter, take your time and look what are things people are linking via twitter. Try to get a good look before kick starting. This will give you a good feeling and experience how twitter can be used. Search for few articles on Google about using twitter.