Even if people have identifed a lot of possible ways how to use twitter (17 ways you can use twitter), I imagine for most people only a few real ways exist. I tend to use it as newsticker (following a lot of official twitter-newsposters, retweeting the most interesting links/news) and to post interesting links myself & to post a link each time I update my blog. I use twitterfox as twitter-reader, its a fast, nice and easy-to-use firefox-plugin.
If I wanted to use it for conversation, a lot of the followers who like to read interesting links would just unfollow – I don’t like to read “my cat just made a cute sound”-tweets myself, if I don’t know the tweeter personally. Therefore, you could and should use multiple accounts for related stuff. I just created @timdellas for my private tweeting and protect the updates there, to not let everyone read the stuff I’m writing there. I hope my friends catch on to twitter soon, then it makes sense to use something like this.
Much of what twitter can give to you is dependent on whom you follow and what these people post. Some lists of you you could follow when you’re starting to go on twitter are online, I can definiely advise to follow @guykawasaki. Then you should look out for twitterers in your city or surrounding, I used twinkle (a location-adding twitter-tool for the iPhone) for that. If you don’t use an iPhone you can take a look at the twittertools-masterlist to find a fitting tool for this or just use the twitter-homepage.
After that its all open. You can click through follower-lists in twitter-profiles, that seem to be interesting for you. Look at mine for example if you’re interested in newstwitterers. Then you’ll surely find lists of people that might interest you soon, like this list of twittering start-up and founders (german).
Hope you’ll have as much fun with twitter as I have. It nearly replaces feeds for me.