Twitter is a microblogging service developed in 2006. What's microblogging? That just means that users are limited to 140 characters per message. There are other microblogging services out there (e.g. Plurk, Yammer and Jaiku), but Twitter is by far the most popular. Although it was originally intended for microblogging, through use it has evolved into a social network and quasi- text messaging service as well.
As with other Web 2.0 applications/social networks, a user first creates a profile, then adds contacts. During this process, or at any time during the life of the twitter account, users have the option of making their profile "locked" or "unlocked." Locked twitter streams are only open to one's contacts. Unlocked Twitter streams can be looked at by anyone. Besides the usual privacy concerns of "not wanting all your business out online for others to see", you may want to consider keeping your profile locked to avoid getting hassled by spammers. The downside to keeping a locked Twitter stream is that people may be hesitant to add you as a contact because they may not be able to get a sense of who you are.
Twitter users have the option of designing the background of their Twitter profile. Twitter comes with 12 pre-made designs, but users can also choose to simply adjust colors or upload pictures to use as a background. Many people who use Twitter for business create a customized background with their contact details, but really, the person who views your Twitter page the most will be you, so pick something you won't mind looking at and feel free to change it as often as you'd like.
After creating a profile, a Twitter user is confronted with an empty box that asks the question, "What are you doing?" If you choose, you can answer that question literally. (Well, maybe not "I'm posting to Twitter" literally, but "I'm working on Project X" or "I'm researching Issue Y" literally.) You can also post a statement or opinion that may be a conversation starter - it may help if you think of Twitter like an online cocktail party where you sort of know people. ("Last night's episode of 'Heroes' was awesome!" or "Watching the Reds game...I think they're going to blow it in the 9th inning again.") Or, finally, you can ask a question of your followers and see what the "hive mind" has to say. ("I'm researching Issue Y and not having much luck...does anyone know of a good Subject Heading to use?")
Twitter is great for sharing information such as web links or pictures, especially if it's something that you couldn't foresee writing an entire blog post about. Since Twitter-ers are limited by the 140 characters of the Twitter box, URL shorteners such as TinyURL are used. There are also format specific Twitter sharing applications like TwitPic. Finally, if you really like something that another person has shared, you can "re-tweet" them by copy/pasting their entire Tweet and putting "RT" in front of it.
Twitter posts, or "tweets", can be a confusing mess sometimes. However, Twitter users cut through this by using "hashtags" to organize their messages. (A hashtag will looking like the pound sign followed by a word - e.g. #subject) Frequently used hashtags will appear on the right side bar of the Twitter screen under "trending topics." Another handy use for hashtags is to organize tweets about an event such as a conference. (e.g. Do a Twitter search for #aall2009)
The web-based Twitter page is not your only option for participating with Twitter. There are several desktop clients and smartphone applications available. People like these because they are often more responsive than the Twitter page (if too many people try to tweet at once, the system crashes and the "Fail Whale" appears) and allow for organization of contacts. They do require permission to download to your computer, so you may have to check with your IT department.