We learn by going where we want to go. - Julia Cameron, The Artist's Way
White belt level
There are a number of ways to get a crack in this field. All of them are valid, and depends on what you will make out of it.
If I were to start over again, I would first learn how to tap into that creative source in you. I'd do this with regular writing practice. The best way to do this is to do Julia Cameron's morning pages.
In a nutshell, you write three pages of stream-of-consciousness writing. You do this first thing in the morning, everyday. Write whatever comes to mind. No editing. Even if it sounds ridiculous and wouldn't make sense, write it. No one has to see this. You can choose to delete them soon as you finish them.
Learn the basics
Once you have that connection to creative source, the next step is to learn how to write effective copywriting. If you are resourceful, you will find a number of sites that will help you with this process.
There are a number of good copywriters who maintain a blog or website. They offer tips and tricks to help you get started. I will recommend that you bookmark their sites, better if you can subscribe to their RSS feeds.
There are also a number of writer forums that you can join. Professional copywriters often hang out in these communities. Newbie writers are encouraged to offer their copy work for critique from the communicty. Plenty of lessons to be learned from this process.
Pick one or two methods on writing copy, then build on that foundation.
Start your business
When you have the basics under your belt, start building your portfolio. Offering your service as a copywriter on fiverr is a good way to do this.
For one, people that hire copywriters on fiverr are not looking for top notch work. They just need someone who can help them come up with something. If the copy converts, well and good. If it doesn't, it only cost them five dolloars.
You can choose to work on one project each week. If you have more time and want to hone your skills, take on more assignments.
Grow your clientle
Once you have something in your portfolio, open an account in odesk or elance and offer your copywriter services there. This time, you can charge a higher fee as compared to fiverr.
Build up a good reputation on these sites, and while you are doing this, start growing your client base.
Do these for 24 months, as you consistently improving on your skills. Next thing you know, you have a profitable Copywriting business for yourself.