Well, there's nothing much you can do with twitter other than using twitter card over your website, and be regular with posting updates over twitter make sure you run some contest giving away some freebies over twitter, as this will escalate more user interaction over your twitter page!
First of all, you need to complete twitter profile with cover picture and all.
If you have a website blog, you can tweet regularly, and share your new posts. It will automatically improve user engagements. Gradually, more people will start following you. Also image and videos tweets can perform much better.
You can use Twitter to help with your SEO campaign. You can create good content that people will want to share. Engage with your followers and attract new ones. You can also improve your website traffic through it. Use hashtags with most number of searches. And take advantage of what is trending.