Here's how you start a career in copywriting.
1. You need to be able and enthusiastic. You have to love writing copy more than anything else.
2. Start by learning the trade: there are various courses out there, of which mine is just one: http://www.inst.org/copy
3. Work as a freelance initially. Do jobs for free or a small fee for friends, neighbors and relatives. Then move on to small local businesses. If necessary, tell people you're a copywriting student. Tell them what kinds of words you could write for them, for example flyers or extra web pages. Most businesses don't realize what marketing they could do.
4. This way, you should build up a portfolio, which you can put on your website and show to a prospective employer.