There are many companies out there who provide a quickfix service in getting you an increase in followers using 'bots'; robots that will flood your system with spam.
If you want to engage with real people and a real audience you should:
Promote your twitter page outside of twitter. If you have a blog, provide a link to your twitter accounts and other social media such as Linkedin, Facebook, YouTube etc. If you leave a comment on forums or wiki's make sure their is a link to your twitter account.
If you have a webpage make sure you add the 'Follow Button' to your pages so that readers can easily be added to your followers list.
Add your Twitter address to your business cards. Beware - remember that people from the business community may be reading so keep your tweets sensible.
Engage in conversation with people who have a lot of followers in the hope that they will re-tweet your message, this may have the impact of boosting your followers as you will be seen as a 'reputable person to follow'.
Discuss whatever is in the trending topics; if you say something witty and insightful that tweet will get re-tweeted and could increase your follower count.
FollowFriday – send out FollowFriday tweets of some people you are fans of and maybe one day they will do the same back for you!
Write good content