Dave Parry at academhack has a recent and very good post on how to actually set up a classroom of students using Twitter. I'm going to use Twitter in my "Your Digital Life" class this Fall and following these instructions will make it much easier for me to get the students off and running.
In other Twitter-related news, I'd like to point you toward Twistori for some conceptual art made out of tweets and to hashtags.org for information about putting metadata in your tweets.
For Twitter alternatives, in case I haven't mentioned them previously, check out Pownce, Jaiku, or FriendFeed. The last is an attempt to aggregate all of a person's social networks into one spot. I've set it up so people watching me in FriendFeed can see my activity at Twitter, Blogger, Flickr, del.iciou.us, and more.