You posted your question 8 years before the date of this reply. By now, hopefully you have found good sources, clients and/or employers and have become an old hand at copywriting. Some individuals have entered the business and risen to run ad agencies in less time than that.
Nevertheless, I'll try to augment some of the earlier answers. You entered the field at an "interesting" time, and it has become even more "interesting" since. With enlargement of the communications world, to include social and other electronic media, and correspondingly less print, it has become the latest cottage industry. Anyone with a word processor now considers themselves a writer. Some are great at it. Some are chasing a dream that they may or may not reach. Maybe some are the ones asking, "Why don't my ads work?" being prime marks to be sold courses and "templates."
So I put it in quotes rather cynically. Being a copywriter, especially in editorial or advertising work, has always offered a lot of variety, the chance to learn about various products and services and to reach readers, listeners and viewers at a visceral level. But it's a highly competitive business, and even if it has expanded, as with the acting biz, there may be more balls in circulation than there are slots to easily fall into.
But to expound on the answers:
Write on assignment, as much as you can. Preferably in a position that gives you some variety, both to make your day more interesting and to broaden your ultimate range of opportunity. Learn to write, learn to get past writer's block, learn to write to spec, and -- above all -- learn about marketing. If it's not selling something, it's not copywriter, it's just writing. Not that there's anything wrong with that, but purely creative writing is a different industry and may not pay the bills.
Although you might find a trusting client willing to hire a newbie, you'll get the needed experience and portfolio much faster and more deeply with a full-time job.
But to get that job, you'll need a portfolio. Various books describe what goes into a top-notch portfolio (anything less than top rank will be problematic). Maxine Paetro has written a good one. It was current when you posted, but I don't think it's been updated to reflect the current scene. Also, it addresses only the Advertising industry, which is only part of today's copywriting scene. Check with Amazon and at your local career reference library. Bob Bly's book i another classic, and surely there are others. Just bear in mind that opportunities for writing marketing communications are very wide, and you might prefer one type of niche or type of industry more than the one any particular book is about.
You can find courses online, but beware of mills and templates. Yes, you might turn out to be the next famous Direct Mail maven, but there are only so many of those. Again, like acting, the business is not just about the core capability (writing). It's also about running a business, keeping up with social trends or technology and whatever industry(ies) you happen to specialize in serving. Briefly, don't pay a lot for a course, but learn what you can from the free ones and move on.
To fill out your perspective, subscribe to AdAge.com and the major trade "paper" sites. Also join your local ad club or copywriting club. One longtime association is The One Club for Creativity (originally it meant "The one club for art and copy," an alternative to clubs focusing on only one of those disciplines), which has a division for students and juniors: https://www.theyoungones.org .
If you live near a university or in a major city, check schools and businesses to see what courses are available. For example, when I was already a copywriter, but needed to network and upgrade my work, I took concept courses at New York City's School of Visual Arts, and from leading creatives at major agencies (through various professional organizations). These are one-shot, a la carte courses, not for a degree. Essentially, the teacher assigns a product, you come back next session with a speculative ad for it, which you present to the class, and the class discusses it. The focus is on your concept, not the body copy. Top ad agencies and other major employers are looking for conceptual thinkers, people who understand consumers (be they average people or business people) and know how to present products in fresh, persuasive ways. Although in the case of technical products there is some need for technical understanding, they aren't really looking for someone who merely writes, comes up with puns, is overly proud of a turn of phrase, or imitates what's already been done. They can find people like that on any street corner.
Take some of your learning experiences with a grain of salt. There is seldom just one way to do anything. Someone else may have come up with a better way than you, but that doesn't necessarily mean your idea was bad. Also, bear in mind that a great Creative Director is not necessarily a great teacher, let alone a mentor. If you're lucky, you'll find a boss or even a client who mentors you to stand more firmly on your own. But a teacher of a course might hold your idea up to ridicule. Whether or not they are right that your ad sucks, that isn't the right way to teach. Consider it a demonstration that the copywriting business, like life, isn't always fair.
Somewhere above, surely you'll find (or have found) a lead to the type of course you were seeking.
I have a further bit of advice at my own site's Copywriter FAQs About Advertising.