This question came up on a thread in r/writing on Reddit from a writer trying to attract followers on Twitter. Although my answer is geared therefore towards authors who tweet, I think it's good advice in general for anyone seeking to establish a genuine online presence on Twitter that's worth following:
- Don't just follow your friends/followers! Use a Twitter client that allows you to monitor multiple hashtags- follow tags like #writing, #amwriting, #abna (Amazon Breakthrough Novel Awards), #litchat, #pubwrite, #authors, etc. Hashtags are conversations. Don't be afraid to jump in, reply, and retweet, but don't go crazy and blow up peoples' tweetstreams with multiple serial RTs and replies all at once.
- Tweet about a variety of topics. This might sound a little counterintuitive, but writers who tweet about nothing but writing are boring, and run the risk of coming off as shills. Tweet about other things that interest you- for example, I like to tweet about libraries (I'm a librarian), D&D and gaming in general, the Boston Red Sox, and how the Massachusetts Bay Transportation Authority ruins my commute pretty much every other day. Not only will you pick up more followers this way, but it also helps your real personality shine through online and makes your tweetstream seem like less of a marketing gimmick.
- Do not automate your tweets- this may work for larger organizations but it's never a good idea for an individual. Also be careful about overly clogging your tweetstream with third-party app tweets. No one will begrudge you the occasional Foursquare check-in binge, but if most of your tweets are coming from apps people are simply going to tune you out.
- Direct Messaging strangers is creepy. Just don't do it!
- Share links to interesting and informative content. Reddit may have seen it all already, but never underestimate the RT power of a quality cat meme. I follow a ton of RSS feeds in Google Reader, which makes it easy to share content out to social networks. If I found something worth reading, chances are someone else out there on Twitter will as well. The internet is such a wild and woolly place that people who help make sense of it for others are valued in social networks. If you establish yourself as a thoughtful digital curator, people will follow you.
- Be authentic in your tweets. As much as it seems to be driven by celebrities and Trending Topics, Twitter does actually reward original expression and the clever turn of phrase. Think of a RT as an upvote here on Reddit and you'll get the idea. Have opinions. Make jokes. Show some genuine emotion. Provide running commentary to that morning's episode of The Price Is Right (helpful hint: people on Twitter LOOOOOOOVE Plinko).
So that's pretty much how I've built up a modest Twitter following. It won't happen overnight, but you'll be surprised how tweeting on a consistent basis on a wide range of topics will translate into a steady trickle of new followers. The key is engagement. If you don't put anything into Twitter, do not expect anything substantive out of it in return.
Enjoy! And happy tweeting...