This is the simple five steps you can follow to get to Twitter heaven:
Get an account - a simple first step
Observe - Watch what is happening, spend time looking at different profiles.
Follow people - Actively connect to people/organisations you find interesting. Then look at who they are following and also look at who is following them ... connect to those you think interesting. If necessary you can always unfollow them later. There is a lot of following and unfollowing in the twitter-universe.
Engage - When you find a post which is interesting retweet it (RT). This is a first tentitive step to engage with your audience.
Engaging - Create new a post on a topic your interested in.
There are a number of tools you can employ to make you life easier