Grief, I really am becoming a Twitter bore... but anyhoo... here is my quick an' dirty list of things which make Twitter slightly less annoying than sitting in the front of the class whilst everyone behind you passes notes and whispers whilst you can't follow what they're saying...
1. Use a browser like Flock which has a built in facility to display and update Twitter in a handy dandy little sidebar
2. Try a desktop client which can sit happily in the background and colour codes entries so you can follow what's headed your way and what's just 'blah'. Twhirl seems to be a goody for doing just this!
3. Find some people to follow who actually have something you might find worthwhile reading. Tweetscan can find entries by keyword - and it's always worth bunging in any old terms to see who's moaning about their boss / work for a laugh. :o)
4. Learn the lingo. There are certain features which will make using Twitter make more sense. The '@' function is one of them... and other useful ones are tucked away and listed as being Twitter nanoformats - yes, it's mildly geeky, but worth a look if you're shy of something to do for a few milliseconds.
5. Look at the alternatives - Pownce, Jaiku, even Facebook status updates... see what else is out there and do a little comparing an' contrasting. The simplicity of Twitter is strangely refreshing.
6. Toddle back to Twitter and decide to find out what other people are saying about it. Web 2.0 Teaching tools entry on Twitter is a great place to start looking if you're interested in using it in education... and then have a wander through the links they suggest. It'll get you thinking at any rate!
Twitter. Not sure. Use it with Flock and Twhirl and see what you think!