I've heard people buying Twitter accounts with large followings and then migrating their username over. That's one way - although I don't get that at all.

Other people have done it with Follower farms .. were they join a follower farm site, and essentially everyone just agrees to follow each other.

Both of these are in violation of the terms of service and may get your account suspended/banned.

The best way to grow your audience is to share things worth sharing. Either quotes, pictures, interesting / funny insights, etc.

I'd rather have 1000 true fans than 200,000 bot followers.

Most of the people who have hundreds of thousands have been on Twitter from nearly Day One and were extremely active, are celebrities of some sort (big-name journalists, actors, musicians, sports figures, etc.), or bought followers.