Before I provide some strategies, here is the barebones, old-school way people have gotten followers:
It definitely works, but the relationship value is almost zero. Here are some better ways:
Twitter is a strange beast. In my experience, the best way to get followers is to engage in, and add value to, conversations.
Having a gazillion followers isn't the goal. Having followers that you can/do interact with is the aim. Search for some of Gary Vaynerchuk's videos about using social media for more inspiration.