While I don't have the most followers on twitter, I've been able to almost double the amount of followers I've had in the past month (I went from 2,500 to 4,500 & counting.) Here are some tips to increase your followers quickly. (All of them are free, they just take up time.)
1. Follow Back - Let's face it. Unless you already have a large fan base outside of twitter, no one is going to want to follow you, unless you promise them something in exchange. So write on your bio that you "Follow Back" and then regularly follow back people who follow you first.
More people will find you and follow you without any action on your part if they know you'll follow back and they'll stay your followers for longer. But if you promise to follow back, make sure you do so promptly. Don't lie about it. That's how you get blocked. And don't unfollow them later if they follow you back, in order to "trick" them. That makes people really angry.
You don't have to follow back everyone. I don't follow back porn stars and porn sites that try to follow me regularly, for instance, but you should follow back 99% of people.
Don't ask for a shout out in order to follow back people. That's an extra step that people might not be willing to take, not to mention, I've given shout outs to enough people (and followed them), who didn't want to follow me back that people like me don't want to bother trying anymore.
2. Give Back - When you are following thousands of people, you won't have time to read all their tweets, even if you sit around all day, every day, doing nothing but reading tweets. But you should still make time, a few times per day (if you're short on time, you do it at five to ten minute intervals inbetween doing other things through out the day) to read tweets on twitter and interact with the people you are following.
I used to be stingy when I favorited tweets. I thought they had to be truly superb before I did so. Now I use the "favorite" button like the "like" button on facebook. Any time I see something funny or intelligent or something I can relate to on twitter, I favorite it. I retweet things that I think my followers might find interesting. I respond to people and start conversations.
Every time you do this, you make the person you responded to feel special. They'll be happy they decided to follow you because of it and more likely to buy your products (if you're selling something) or to want to talk to you (if you're just there to socialize).
3. Look at people with lots of followers - If you find someone on twitter who has 40,000 followers and is following around 40,000 people, then you can tell this person is good at finding followers who, in turn, follow them back.
This is something you need to do as well. Twitter has limits about the amount of people you can follow, but every time you gain a follower, that number rises. What I do, is follow around 500 people, wait a week to see how many of those people follow me back, and then unfollow the rest. Then I start all over again.
I find these people by looking at the followers of people who have thousands of followers and are following thousands of people as well. A higher percentage of those people follow me back than random people I find on twitter.
I also keep the number of people that I'm following who are not following me back, relatively low, like 100 or so, otherwise twitter won't let you follow people back or add people.
4. Justunfollow.com - I use this site almost every day. It helps me keep track of who I need to unfollow and who I haven't followed yet. I couldn't use twitter as well without it.
There are similar sites and you can try using those, but this one has been the best I've found.
5. Don't advertise all the time - As people get to know you, they'll eventually find out about your book or product as well. They'll be more open to buying it if they like you as a person first. If they never interact with you and all they see is advertisements coming from your account, they're likely to get annoyed and block you instead.