How can small businesses successfully use Twitter?
Are people being successful? Yes, but it all depends on what your goals are.
Twitter provides an immediate, current commentary on--well, on just about everything. If it's about your brand, then you need to be listening, and reacting.
Many companies are now monitoring Twitter for complaints or unhappy commentary, and quickly reacting to solve the customer problem. I use Tweetdeck to monitor for mentions of our products, although there are probably other similar tools.
Pragmatically, though, if you don't have a well known brand then you won't see a lot of people tweeting about you specifically. You may well find people Tweeting about related companies (larger competitors, national brands) and topics that relate to you. You can help build your own visibility and following by participating in--and initiating--these discussions.
Overall, though, I'd encourage you not to mix up your goals and your tactics. Twitter can be a good tool, but it's a tool. I don't want to sound like a luddite (or worse, old) but most small business owners have more important things to do. So make your customers happy so that they'll talk about you--let them do the tweeting!