Building popularity on Twitter is about gaining followers, and the most fundamental and important concept to learn about building popularity is the idea that when you follow someone, they'll get an email about it and there's a good chance they'll follow you back. If that doesn't work, try responding with an @ to something they said. If they check their "replies" stream, they'll see it and possibly follow you.
Once you've got that down, the rest is gravy. But you can also use Twitter to build up a bit more authority on social news sites. Below are a few more tricks to get you started:
1) Match Your Usernames and Avatars
Most social news sites allow users to have an avatar associated with their account and they all use usernames. When you setup your Twitter account make the username match your social news username, and use the same avatar as well. This way, when someone who's familiar with your account on another site sees your tweet it will catch his attention.
2) Search Twitter for Twitter Users Mentioning Your Favorite Social Site
Log into your Twitter account, and search for the name of the social site you want to be more popular on in the "Find Folks" box on the right. Go through the results and follow active users who seem to like the same site(s) you do.
3) Search Google for Profiles on Your Favorite Social News Sites Mentioning Twitter
This is similar to the last trick, but this time, go to Google and type in: site:digg.com/users "Twitter" "StumbleUpon" and you'll see a lot of Digg users with Twitter accounts, who have linked to Twitter in their user profile. Follow the link to their Twitter profile, see if they're still active and follow them. The reason you're searching for StumbleUpon as well is that it increases the likelihood that Google will return results where Twitter appears in the About section of a user's profile -- try substituting StumbleUpon for other social networking sites to change your results set. You can try this trick with any social news site.
4) Link to your Twitter Account from All Your Social Profiles
Make sure that a link to your Twitter account appears in every possible social media profile, blog or social network page that you have. If someone you know from a social site is on Twitter, you want them to know and be able to follow you easily.
5) Ask Readers of Your Blog to Follow You
If you have a blog post or other piece of content go popular on a social site, ask readers to follow you on Twitter if they liked what they just read. This will increase your presence on Twitter, which will help increase your profile elsewhere.
6) "Twitter-jack" Active Social News & Twitter Users' Friends
When you find a popular Twitter user who's also using your social sites a lot, go through the list of people they're following and follow them too, look especially close for names and avatars you recognize from those other sites. This can be a recursive process, take hours, and ultimately lead you to a lot of new Twitter friends.
7) Ask Questions
When you ask a question and one of your social media savvy followers responds, his (probably also social media savvy friends) might see him talking to you and come follow you too. This is a more passive version of the Twitter-jack mining technique described above.
8) Don't Just Spam Twitter, Add Value
Of course this should go without saying, but don't ever spam Twitter. If all you do is constantly drop stupid Digg links all day nobody will follow you for very long, so make sure you're actually adding value, not only by tweeting cool links other than your own, but also join the conversation. Congratulate people, answer questions, say hello to new followers, be social.
9) Post the Title with the URL
If you post a URL to Twitter that is too long, they'll shorten it with tinyurl for you. This means that no one can see the source link and get an idea of what the page is before clicking it. Preface any links you share with at least the title of the page, if not a short description as well.
10) Consider Using a Social Media Specific URL Shortener
If you're trying to get more popular on multiple social news sites, the tendency may be to post a link to the story on every social site you want it submitted. This will annoy your friends and followers. Instead, try something like Votrs.com which will not only create a short URL for tweeting long links, but the landing page will also include buttons and badges for easy submission and voting on various social sites of your choosing.