Twitter can be a scary place for beginners, but don't be discouraged if you only have a few followers after the first week. There is a great way to get tons of followers that legitimately want to follow you.
Step 1: Search for people that have the same interests as you. If you are an author you want to search for these: books, authors, writers, reviewer, book blogger, book lover, publishing, and other book related words and phrases. Also search for the genre or genres you write in. The search will lead you to people who tweet about this stuff. Follow them.
Step 2: After you've followed these people, retweet them. By retweeting some of their key tweets, you are both endorsing them and telling them that you care about this stuff too. When you retweet, you will not only get followbacks, you'll start to gain followers who notice that you retweet. These people will follow you in the hopes of getting a retweet themselves.
Step 3: Start tweeting about your own blog posts, books, interests and other stuff. Be sure to keep some tweets personal. Don't over do it on the promotion. Remember all those people you retweeted? They can now begin to repay the favor. Twitter is about the balance of give and take. The more you give, the more you will get in return.
Step 4: Don't forget to have actual conversations with your followers and read their tweets too! Keep the social in social media!
There you have it! If you want real followers who actually care about what you tweet, follow these simple steps and avoid the temptation to buy followers. Most of those are scams anyway.