Okay, so you've registered an account and set up your profile. You now understand the basics of Twitter symbols / language. And you're most likely following a few people.
Of course, Twitter is useless as a marketing tool if you don't have followers, so this should be your main objective.
First of all, go to Facebook, MySpace, and any other social networking sites you use. Post a link to your new Twitter account in your status update, urging people to follow you.
In your email, put the Twitter link in your signature, and do the same for forums (the Warrior Forum will put your link in a Twitter symbol under your username and avatar).
If you already have an email list, send out a blast talking about your new Twitter account and encouraging them to follow you. If you have a blog, write a post about it. If you use WordPress, you'll also want to install a plugin that will easily allow your visitors to follow you. I'll cover that in more depth later on.
Basically, make your Twitter account visible wherever you have an internet presence.
Another way to gain followers is by simply following others. When you follow someone, they are notified by email. Very often, they'll be curious about you, check out your profile, and likely follow you back.
However, you have to be strategic. Don't expect results by following celebrities or extremely popular users, as they probably won't even notice you. Don't follow random strangers – why on earth would they be interested in you or what you're selling anyway?
One awesome function of Twitter is the ability to search what people are talking about. If you have a blog about gardening, you can search the keyword “gardening” and it will pull up everyone Tweeting about gardening.
Keep in mind that you can only follow around 2000 people each day. It sounds like a lot, but if you use the Twitter search engine you might reach that limit sooner than you think. There are various programs and online services that allow you to follow and unfollow people automatically, rather than going through the process manually (which can be an extremely tiring, boring process).