How to utilize twitter to get the best results?

Try to post effective contents with Hash Tags that can help you with a better outreach.

-Engage with followers, actually @ them to say hello, good morning, reply to a relevant tweet, start a conversation.
-Compose tweets that require response - like questions or polls.
-Hold a giveaway competition to drive those followers to your other places eg. website, FB shop etc..
-"RT if..."
-Take a look at their accounts - why do they follow you? Give them more of what they want.
-Make sure a link to your website is on your account to drive that traffic.
-Research some influencers on Twitter. EG. If I had an account on mens fashion, I would contact menswear instagram models under certain followers count to arrange exposure deals etc...

Writing the quality contents which are highly interested into the followers.

Doing some contest to make the good interaction with peoples who followed the account.*

Asking some questions to get the engagement.*
Sharing the contents with the help of trending hashtags.

Sharing the posts which get more RT by the followers.

For best Twitter results:Optimize Twitter bio, Find out influencers and experts on regular basis, Get colleagues involved, Tweet regulary, Track and respond mentions, follow trends, hashtag and use images/videos, Use twitter analytics

Engage in trending topics with creative and appealing content.

Tweet regularly and follow trends/hashtags.Use maximum possible images in your tweets because images are eye catching as compare to the text! Thanks.

2000 followers is a very good number for starting in Twitter.
People has already given you some good advice on how to continue, ill just like to repeat that using trending topics and images are very good for getting more engagement.

Ty everyone for your advice.

Sounds pretty good. You have 2000 followers, so share useful information to your followers. Based on their business to share information.

1. Infuse personality into your profile
People trust people, not default profile images. Use a real picture of yourself and infuse your unique personality into your bio. This generates interest and encourages people to not only follow you but relate to your passions and keep an eye on your tweets. It all leads to more retweets.
2. Be the first to break the news
Choose a topic (or several topics) that are near and dear to your heart and consistently provide valuable information. That will allow you to position yourself as an expert in that area and your followers will come to rely on the valuable information that's hitting their Twitter streams.
If you stay on top of the latest and greatest, try to break the news to your followers as you get it. That will increase the number of retweets you get and will foster the conversation around your news.
3. Tweet consistently, leave space
I recommend tweeting consistently. However, most of us choose a time during the day to catch up on the news and do some research. We come across multiple data points and links that we want to share with our followers.
But sending 15 tweets within the same hour may be overwhelming to your followers and may be considered spam. So, I suggest you schedule the tweets throughout the day with at least 30 minutes between them.
4. Ask and answer questions
Asking your followers a question is the best way to engage them (and get some valuable information in the process.). But if you want your followers to engage with you, you need to engage with them. Answer their questions, share your knowledge, participate. Also consider engaging in chats. Twitter becomes more beneficial to you when you provide value to others.
5. Connect people
Be a connector, in real life and on social networks. When you connect people with each other, your followers take notice and your credibility goes up. People are more likely to engage with you.
6. Be generous, promote others
Make sure you retweet your most passionate followers. Thank them and link to their social properties. #FF and #Recommend others and their work.
7. Craft your tweets
Make sure your content stands out. When you retweet, customize the copy and add your own thoughts. When you tweet the link, choose a quote or statistics from the article that you thought was impressive or interesting and tweet that instead of the headline.
8. Use under 140 characters
If you want to be retweeted, leave the room for others’ Twitter handles. Some folks prefer the old RT style to the new one. They retweet you more if you leave space for their handle and a little space to add their short comment.
9. Ask for a retweet
If you ask your followers, “please RT,” you usually see higher number of retweets.
10. Acknowledge the source
Always, always acknowledge people who shared the information with you, even if they shared it through other channels. If that person has a Twitter handle, credit them as a source.
11. Tweet the same content again
The Twitter stream moves very fast. There's a good chance that most of your followers won’t catch your first tweet. If you stumbled on great information or you want to share your own content, schedule multiple tweets in advance during multiple days. If your followers are spread across the globe in different time zones, schedule tweets during different times of the day.
12. Be open to new connections
Follow people back. This allows them to connect with you personally through DMs. And you expand your social network. I've made many invaluable contacts just because I was open to new connections.