I know there are professionals who tweet for money, but I just dabble using various services. If you would like to try using your Twitter account for money, I'll tell you my experience.
My favorite service is called Sponsored Tweets. I recently made payout ($50) and the process is really simple. They send you emails when there are ads that match the type of things you like to tweet about and you write a tweet for the company. I love how simple it is and they have a lot of opportunities. You can either get paid for every tweet you write or you can get paid per click. I've found that the flat rate pays more.
I am also a member of Magpie. Magpie tend to pay way more per click than Sponsored Tweets and it has a pay-per-lead option, which means the person has to sign up for something. One of my pay-per-lead ads pays $66 per lead. Not too shabby. The only problem is that the site doesn't provide a flat rate fee.
Today I signed up for My Likes. This site works a little differently. Not only can you make money off your tweets, you can also make money by posting on Facebook and YouTube. Here, you can either write the ad yourself or automatically post a pre-written ad. It seems fast and simple.

Are you a member of any of these sites? If you are, let me know how you're doing.
ETA: Here is an updated on my tweeting for money progress with these sites.