The first - and most effective - way of growing followers is to Tweet on a constant basis... but that's not the only technique you should use. Your next goal is to follow and list other people by going out and finding them, rather than waiting for them to come to you.
This is actually more important than it sounds. As noted in Robert B. Cialdini's The Psychology of Persuasion, "The rule says that we should try to repay, in kind, what another person has provided us..." In short, people feel obligated to reciprocate when you reach out to them. They might never normally think about following you, but when they receive a message saying that you're paying attention to them, then chances are they will seriously consider following you in return.
However, there are two major guidelines to reaching out to others, and both of them are important if you want to truly succeed in gaining popularity on Twitter.
Follow Who You Care About
You should never extend your efforts to following people that do not matter to you. This includes bot accounts, customers outside of your target range, unrelated businesses, and anyone else that you don't have any need to reach. Many of these people will not follow you in return, and your efforts to attract them will be wasted - worse, they'll throw off your analytics and stop you from understanding the users you do care about.
It may be tempting to simply purchase followers and give yourself the appearance of a valued member of the community, but this will also stop you from reaching the people you're trying to reach. In short, use good judgment when deciding who to follow on Twitter.
Obey Twitter's Guidelines
It's also easy to rush into things, hoping to build your number of followers as quickly as possible. Avoid doing this - following more than a certain number of people per day could result in your account being flagged as a potential spam-bot - and take days to resolve. Following new people at a steady, reasonable pace is the best way to increase your presence on Twitter without coming across as a company that simply spams others.
In the same vein, try to avoid spammy posts and focus on topics that are important to you, your business, and your customers. When necessary, link to your blog.
For Better Results, Use Lists
One of Twitter's most valuable functions is the ability to create lists of users. Sorting your most important followers onto lists can help you keep track of things and reference information when you actually want to have it - for example, you could set things up to check tweets from your employees on one page, while another page might focus on local news that's relevant to your daily operations. Use lists whenever you can - getting a message that they're now on a list can make people feel more valued and encourage them to pay attention to what they have to say. It may be difficult to think up unique names - Twitter currently supports up to 1000 different lists - but you should try to avoid list names that make people think they're not special.
If you're having trouble with names, ask your employees to each submit a list of ideas for your consideration. This should give you options for quite some time - each list's name should be short and descriptive, enough to allow you to easily remember what sort of people will be on it. If you feel like things are getting out of hand, then record descriptions of lists elsewhere and reference that document as necessary.
