Here I will give few tips of how to organically/naturally increase the number of your Twitter followers. If you are simply looking to increase the number of followers, not real readers you can use some automatic tools for that. If you want to grow the number of readers, quality followers, the steps bellow are designed for that:
(1.) Come up with short and good name: Since your Twitter name is part of Twitter search, make sure it includes the most important keywords, explaining what your Twitter users is all about. Currently Twitter allows up to 20 characters, try to utilize them all.
(2.) Make a good avatar: The avatar is first thing your twitter visitors will be looking into. Make extremely creative Twitter avatar, make it eye catching and interesting, as well as presenting who you are.
(3.) Write up a good bio: Extend here your Twitter name, write in more details about who you are, what are your interests and what you will be tweeting about. When you write your BIO use following rules:
(1) Utilize max allowed characters. Currently you can put up to 160 characters.
(2) Do not repeat your name.
(3) Try to use as much as possible different keywords that people may use while searching content like yours.
(4.) Tweet well and tweet often: Try to Tweet constantly, at least several times a day. Write nice short messages, not just "Hi", "Hello", "what's up?". Re-Tweet, reply to others tweets.
(5.) Ask people to retweet you: If you can of course, ask your followers to retweet you. That way, their followers will see your tweets and some will also follow you at some point.
(6.) Search for tweets with keywords related to your topics of interest:Leverage Twitter search to find other users posting similar tweets so that you follow them and there is good chance they will follow you back.
(7.) Use hashtags: Use hastags (#) in your tweets. Don't put hash tags for every words, as it will be very hard to read your tweets. Put hashtags on main keywords in your tweets. It will help others to find your tweets and your user.
(8.) Put up "Follow me on Twitter" links on your blog, social networking profiles, wikiHow user page, email signatures, etc: This is self explanatory. Put follow me button on your website or blog, put follow me link in your email signature, forums and other social networks.
(9.) Follow people who follow people who are like you: Search for other users based on your own keywords. Follow these users and there is good chance they will follow you back.
(10.) Make an effort to keep your followers on Twitter: Try to be in touch with your followers, send them DMs, retweet their tweets, or reply on their tweets.