For those that need a rough primer on Twitter:
Basically, you create an account. In the profile for the account, you tell a little about yourself, give a website if you have one, etc. You can also link it to your Facebook account, although I've never done this since I never had both a Twitter and FB account at the same time.
From there, you can "follow" people, whether they be friends, corporations, non-profit orgs, really anything with a Twitter account. When you follow that person, anytime they tweet a message, it shows up in your Twitter feed. The feed is a timeline of messages from all the people you are following.
The flip side is also true. If you write a tweet, then anyone who follows you will see your tweet under their Twitter feed.
The somewhat unique thing is Twitter is meant for short messages - 140 characters or less.