One of the built-in tools in Twitter is the ability to text message to your Twitter account from your phone, and many Twitter users do this. There is a page in Settings that allows you to create this ability. I don't use it because I can barely see well enough to make a phone call on my cell, much less text message. That doesn't mean it's unpopular with other tweeple. Many updates are sent to Twitter in this way.
There are other third party applications to organize Twitter, which is in itself a fairly simple and straightforward arrangement. Some of those more sophisticated applications like Friendfeed are mentioned at this blog.
As your Twitter following grows, you might want to try some of these tools to see if they help keep your Twitter account more organized. Me? I tweet on my computer, monitor the account daily, and find that this works fine so why mess with success? You, however, might find some of these applications very useful, so by all means try something new and then tell us what works for you and why.