To make money off of Twitter, you need to have an account with a following. The money you can charge is based on a variety of factors. If you have a smaller fan base, but your followers are very engaged with your posts, you can charge more than someone with a large but disconnected following.
To be able to charge clients for tweets, you should build an audience of several thousand followers. Build your following by regularly posting content throughout the day. But most importantly, be social. Reply and tweet to other people to start conversations. Participate in Twitter chats to meet new people and get your name out there.