1. Write Interesting Tweets
The more you generate content people want to read, the more likely it is that people will retweet you. When they do that, then their friends will see you and follow you. Every time you get retweeted, you reach a much larger audience, and the way you do that is by being interesting every time you post.
2. Post On Weekends
A 2011 study found that Twitter users who posted on weekends had higher clickthrough rates (CTRs) than those who didn't. It's tempting to take a couple days off from your social media networking, but people read Twitter on weekends too, so take advantage of that opportunity and reach out to a new crowd.
3. Crosspost
If you have a Facebook, a Twitter, and a blog, you should be crossposting between all of them. Got a new blog up? Tweet about it and post it on Facebook. Got a Facebook promotional running? Tweet and blog about it. If people who follow your Twitter can get an update on everything else, they will.
4. Put Your Blog In Your Profile
You don't even have to link to it in every tweet. As long as your blog or website is available to view from your Twitter page, people will see it when they check out your profile. Making your blog as available as possible is a great way of generating traffic.
5. Search for Similar Users
Don't just sit back and wait for the traffic to come to you. Go out and hunt down people who might be interested in what you have to say. Follow them, tweet at them, and retweet any posts that might be relevant to your audience. They in turn may do the same thing for you. It's a great way to network online.
6. Create a Rewards Program for Those Who Help Promote You
Encourage your followers to tweet about you through a rewards program. Choose the most creative tweets involving you and your business, retweet them, and offer them a reward. A shoutout, a discount, special access to new offers before everyone else - you can choose whatever reward you want, as long as it's something that continues to promote you.
After all is said and done, you've got to remember not to rely solely on twitter to promote your brand. The most popular people on twitter are people who are also popular in the real world. Justin Timberlake, Barack Obama, and Lady Gaga demonstrate the importance of building real world popularity to transfer into twitter followers. Stick with it, make a name for yourself, and the rewards will follow.