There are many ways to grow on Twitter, and the most effective one is through engagement. The idea is to get exposure by finding influencers in your industry and engage with them.
Reply with added value
When an influencer tweets something, you can quickly reply and add some value. If they like or retweet your reply, you will get a lot of exposure! The key here is to add something useful to the conversation. Don't be spammy or reply for the sake of it. If you do everything right, even if the author won't notice your reply, their followers will see it!
As long as you give people a reason to follow you, theywill follow you.
If you have something that might interest a particular influencer and it makes sense to tag them - do it. The key is to find out what their current interests are and then carefully compose a tweet. Big accounts get mentioned dozens of times per day, so make sure your tweet immediately clicks with them.
Just like you, they always look for content ideas. And if you give them what they want - they will gladly quote retweet you.
Most of the time you'll be ignored, but if you get that one notice - it will be worth of waiting, so be patient.
It's also very easy to overdo it by tagging tons of people in one single thread of tweets or doing it often. This will be noticed both by the influencer and their followers and the result of it might be disappointing.
Always reply to your mentions
When people reply to your tweets, their followers see it. It's your free exposure, so if somebody mentions you - reply back promptly. Even if it's not essential!
If you ignore your followers, you can be sure they won't interact with you again.
Another great tactic is to ask questions. If it's an interesting one, people will respond and engage so your original tweet will appear on their followers' timelines. If they become interested, they will open the original tweet to explore other replies.
Use these tips to get more engagement, and you'll start seeing a difference.