Tweet Full (http://tweetfull.com) a tool that helps you get leads from Twitter. Instead of making this post a plug for it, I am going to give away the secret sauce so that you can use it without paying for the tool.
One thing that has worked wonders for me when it comes to marketing on Twitter is to feed my customers' ego.
I used Twitter advanced search to find people who were Tweeting with my keywords of interest. Then I would engage with those Tweets by simply Favoriting or RTing those Tweets. This was not as obtrusive as starting a conversation with them, yet it made them curious enough to check out my profile.
Then I would use a pinned Tweet with a great call to action (20% off right away) that would encourage them to click on my link. I also had a link to the startup/product I was promoting.
My Twitter analytics showed me crazy growth doing this. I was getting 2-3X impressions spending only an hour or so doing this. You can use this method for your own use without paying anybody.
Then I thought of automating it and someone posted on Reddit about Tweet Full (http://tweetfull.com). It had additional bells and whistles like I could search for people with certain words in their Twitter Bios (Twitter search doesn't do that), filter by their Klout score and most importantly ability to pick Tweets with certain sentiment. It is a decent growth hacking tool for Twitter that produces results.
With Tweet Full I am getting over 70K impressions on my profile a month and 1-2% of these people engage with me via Tweets. I use Tweet Deck to keep up with all of the accounts I manage and to engage in a conversation with those who Tweet Back at me. Many times it is automated "Thank you for Fav" Tweets but many a times I have gotten legit customers.
Hope you like it.