I would like to know how I can grow my twitter followers and promote my business using social media
Growing your Twitter followers will require some patience and energy. The first thing you need to do is to make sure you have a regular stream of tweets. Try to post at least one tweet per day but preferably multiple. Each tweet needs to be relevant and valuable for your audience. If you just tweet for the sake of tweeting your followers will quickly start to drop. In the early stages, your organic follower rate will only grow little by little but once you gain momentum large numbers of followers can be gained organically each day. Persistence is key.
When you don't have sufficient content you can share on Twitter you can also share articles from external web sites and blogs. This will help you get the volume while still providing value for your audience. Post url's directly from your twitter account. Don't retweet articles posted on other accounts. When the article get's retweeted it will drive traffic to your account instead of an account you retweeted it from.
A good tip: when you add a url to your tweet put it at the end of your tweet. Twitter will then hide the url and render a twitter card. To know what the card will look like you can test it first using this tool: https://cards-dev.twitter.com/validator (sometimes you need to click the preview button twice for the card to show in full)
There are also some tools like crowdfire that can help you attract more followers. On average the quality of the followers you get from these tools is not that great. Your numbers might go up but the number of interactions (retweets and likes) will not increase at the same rate. It's a good tool to get your initial follower base and make you look like a professional brand but in the long run you want to gain followers that are truly loving your brand.