Pick Your Platform
Explore a variety of apps and pick the platform that works for you. My favorite, Tweetdeck, allows users to create multiple streams in columns. You can create a column based on a hashtag or an individual user. Note: There is currently not a Tweetdeck app for iPhone or iPad, but you can still access it from your browser.
This video is a little long but shares some great ways to use tools like Tweetdeck (and a few others) to get the most out of Twitter. Plus, it was created specifically for educators.
This video discusses the use of Tweetdeck as a tool used specifically for the management of educational Twitter chats.