To use Twitter effectively, it's important to understand how it works. Anyone with a Twitter account can leave a direct message that others can view. If that was where Twitter stopped, it wouldn't be so popular. Twitter users can also reply to other people's tweets. This interaction is what makes Twitter special.
If you respond to someone who's following you on Twitter, the message will be preceded by the @ sign, followed by the person's user name. Even though that person is responding to someone directly, anyone can read the message. Want to keep it private? You can respond by sending a private direct message. But, unless you're following the person, he or she can't respond back. This is why many people choose to keep dialog on their Twitter page.
Read something interesting from someone you're following? It's perfectly acceptable to pass it along, just give credit where credit is due, and acknowledge that it is a "re-tweet." Preface your comment with a RT@ username and everyone will know who you're crediting.
You don't have to head to Twitter every time you want to make a post. One of the beautiful things about Twitter is the number of desktop and mobile phone apps available that allow you to make a quick post to your Twitter account. Try Twhirl, Twitterific or TweetDeck. Looking for something specific? Try search.twitter.com for a list of tweets on the subject.