After creating your user account at twitter.com, install some applications to your computer or phone.
I suggest the following:
Anyone can post a tweet, and (most) everyone can read them, but it gets interesting when you start to connect users, hashtags and searches.
A twitter user can be referred to as @username.
A twitter hashtag can be referred to as #hashtag.
Hashtags are a community-driven convention for adding additional context and metadata to your tweets. They’re like tags on Flickr, only added inline to your post. You create a hashtag simply by prefixing a word with a hash symbol: #hashtag.
Searching tweets (a post to twitter is a tweet) is fairly easy, but people have started programming sites for this as well:
Twitter might also be a great marketing tool:
I simply use it mostly to keep in touch with friends and to follow interesting blogs and people, see for yourself @leonieke : http://twitter.com/leonieke