Twitter is a glorious mess of chatter. Think of it as millions telegraph messages going out to the general public - all at once. There are a couple of ways to narrow down what you want to read and respond to: lists and #hashtags
#Hashtags are great for tracking a current news event. To find people tweeting about the events in Libya, for example, type #libya into your search bar, and see what's being said. You might also notice what other #hashtags are being used by tweeters you like, and check those out. It's possible you might like some tweeters enough after reading a few of their tweets that you'll want to "follow" them (add them to your friends), so that their tweets show up on your own homepage from now on.
Of course, after you've done this a few times, you'll have hundreds people and thousands of tweets on your homepage, and you'll be almost back to square one. Now, it's time to create a list - or a couple of lists. To do this, you'll have to figure out how you want to organize the people you're following. Maybe you just want a list of your favorites, or maybe you want to separate them into business-related tweets versus the more social tweets from people you're friends with in real life. To create your list, go to "lists" in the menu, then click on "create a list, and follow the instructions.
It is possible to make any good thing into an obsession, and if you're in that stage, then you'll want to check out Listorious for lists, and Hashtags.org for #hashtags. Oh, and for your web page or small business, Business Insider has a great read on 11 Ways to Use Twitter Lists to Increase Brand Visibilty.
Jennifer Pointer is in Tulsa, OK. She promotes a simple, a low-tech approach to effective online profile management, search engine optimization and social networking.