I saw an interesting article by David Coursey; he writes "People Try Twitter One Month, Then Fly". That may indeed be true for many people, but they probably haven't found a way to use Twitter to their advantage.
I find that there are a lot of people on Twitter who are looking to monetize it -- primarily marketers looking for the next big thing. I try to avoid those people. You can tell who they are fairly easily -- you get an email (from Twitter [you can turn those off if you want]) that says that someone has started to follow you, but a couple of days later, if you haven't "returned the favor" by following them, they stop following you. These people aren't interested in you - they are looking to create a "following".
To me, Twitter looks like a public IM agent. But instead of directing your message to one person, you publish it to anyone who wants to listen. People who think you're interesting "follow" you (think of it as - they subscribe to your tweets) and you "follow" people you find interesting.
Of course, what constitutes "interesting" is up to you. Personally, I tend to follow people (and organizations) that are into computer security and iPhone/Mac. Sometimes, I have something to say, but usually, I just watch the flow.
So, how do you get started? Check the blogs and web pages that you read. Many will have a twitter link where you can follow either the author or the organization. Start there - follow them. If you know someone on twitter, follow them. After a while, you may find that you're not interested in what that person has to say - easy - unfollow them and you no longer see their tweets.
Next, visit the profiles of the people you follow. Check out the list of people that they follow or the list of people that follow them (if you are interested in them, you may be interested in people that are one degree away from them). Visit their twitter page (click on their name) and see what they tweet about. If you are interested, you can follow them too.
If you have opinions about what is being discussed, join in. You don't have to express every thought that is in your head (unless that's your style, of course); you don't have to say anything at all.
Try it. You may not like it, but you just might.