1. Follow those you're connected to on LinkedIn. You can use Twitter to supplement your efforts on LinkedIn. Check the profiles of your most significant connections to see if they are on Twitter and, if so, follow them. You can even create a list specifically for your LinkedIn connections. Then engage with these people on Twitter: like their tweets, re-tweet them, and comment, as appropriate.
2. Follow prominent leaders in your field. Seek out the thought-leaders and champions in your industry, follow them, and comment on their tweets. Not only will you learn more about your field, but you might just end up with a new mentor.
3. Share your knowledge. Become a resource for others by tweeting out articles of interest in your field, sharing your ideas and experiences, and engaging with your followers.
4. Search relevant hashtags. Stay up to date in your field by searching on topics of relevance or to be in the know about job postings. It's as simple as searching for #[industryorfield]jobs, such as #publishingjobs or #marketingjobs or #salesjobs.
5. Join a career-related Twitter chat. Search for career chats or hashtags on career topics to learn when a chat is happening and then join in to learn something new, contribute your expertise, and build your network.