There's art, skill, and finesse that comes to not only gaining a real audience, but gaining the right audience, and keeping them engaged and sharing your stuff.
The basic strategy stripped down to its core:
Set up your Twitter profile with a description using keywords and include your website.
Follow the followers of other twitter accounts that match the followers you would like to have. You can follow up to 1000 people a day. This is the most important step. Following the people you want to have as followers yields about 11 follows to 1 follower gained. Follow as many people as you can as often as you can.
Set up an auto DM (crowdfire is good) to announce what you're doing to any new followers.
Set up an auto Reply to any new follower (some do this, I don't)
Post quality content
Pin a tweet
Reply to people and engage
Retweet
It takes getting into the habit of hopping on twitter, daily, for 10 or 20 minutes to follow a lot of people, post a tweet, retweet a tweet, like a few things.
(Use Buffer if you want to prearrange and schedule tweets... I personally prefer to go to twitter each day and find something interesting than to line up a series of tweets for the week... but others prefer scheduling)