Twitter's pretty easy, albeit a bit daft in my opinion. Nonetheless, I can certainly see its utility at a busy tradeshow or if you're on campus of an afternoon or similar. So...

Start by going to Twitter.com and clicking on "Get Started - Join!". You'll then see their sign-in window:

Easy enough (though they have an annoying captcha program, but one can only imagine at the spammers eager to automate sending marketing messages (aka spam) to the "twitterstream", so... we all get to suffer). Next step is to send your first twitter:

Click on "Update" after you've typed in your message, and you'll be sending Twitter messages.

Now you can delve into the amazing world of Twitter as you want, by downloading Twitter-related widgets for your Mac or PC, configuring Twitter on your cellphone (far more useful in my opinion than twitter on your computer) and, of course, encouraging friends and colleagues to subscribe to your Twitter stream so they can keep up to date on your latest trivial doingsactivities. :-)

Try it for yourself, check out my Twitter feed. Subscribe by clicking on "follow" on the right, or, if you do a search and find me (which seems easier, actually), you can click on the big "follow" button:

Hope that helps you get going. If you have a smartphone, you can easily just log in to the Twitter site from your phone then bookmark your home page, making it easy to update on the run. Or, failing that, Twitter can use SMS to text message you.