Twitter cannot be compared with Facebook or other Social Media sites. You just have a few text words to fill to get attention and attraction, it is not that easy and hence Twitter requires a completely different point of view.
(Having said that I am not even going to speak about buying followers, it's completely worthless as most of these paid followers are fake running a fake account.)
Informative Posts: There is no secret when it comes to social media (or any other content marketing) but "USEFUL CONTENT" the key is to write some useful and rare contents specially for Twitter. Ofcourse you can say that Twitter allows very few words to develop good contents, yet you need to somehow master the art of creating sweet, informative, interesting contents in shorter format. Good Tweet will get more engagements, they can be emotional, touching, loveable and informative, but remember you have to master mixing it up. To much of one stuff will get boring soon enough, also remember you are here for marketing and not to get empty engagement for ever.
Hashtags: One of the few options available on Twitter is Hashtag, you can surely use it effectively. Just learn what are the most trending "Hashtags" related to your industry and use them accordingly. There are a lot of users who use Hashtags to find posts on Twitter (also on Facebook), and this might bring more engagements and likely more followers.
Twitter SEO: I know you think that I am saying this just because I am an SEO. But no, Twitter gets a lot of traffic from Search Engines like Google, people use hashtags on Google to search for desired tweets. So it makes sense to ensure your twitter page is properly optimized (you don't have to worry about building links).