Go grab the software
http://www.twhirl.org/ it's free, it works like an IM for Twitter. You can monitor the random chats more, then see any messages to you or direct messages sent. Direct messages are like IM or icq messages..
Twitter has lots of tools too, you can post your blog updates straight into twitter, you can post I think all cell phone types, emails, twhirl, other IM's, and so on. Tools to welcome people, find exfollowers, track other stats and so on. It also integrates with most other social sites (like facebook), so you can share your tweets from it to others, or from others to your twitter account.
You can retweet posts you like, to share them with others. Doing it with others expands your base of exposure on your name and whatever you are sharing. And gets others doing it.
You can have 'at least' 90k followers, so your marketing potential is pretty much unlimited.
Don't get me wrong... I'm not a twitter master, but it's growing on me so I'm reading up on it. So if you have any questions, just drop me a tweet or a dm and I will see what I can do to help ya out.