Being a professional artist is not about drawing all day. It is not about painting all day. To make it, you have two paths more or less. Of course there are variations, but for the most part this is what you got.
1) You are part business person, part accountant, part marketer, part artist. In this role you create your work, you reach out to potential clients, you nurture relationships and manage your money from work. You will spend more time on the business part then on the actual artwork. Sometimes that ratio will switch, but count on at least 50/50 for division of time.
2) You score an awesome rep who sells you for you. This rep does the marketing, the business of nurturing relationships, the accounting and all you do is draw or paint. I know, sounds sweet. But don't think this is free, reps need to make money too. Count on giving them 30% or more of what you make. If this sounds good, then by all means go find a rep. Oh, I forgot to tell you, it isn't easy to A) find a rep that will promote you as aggressively as you will, and B) getting a good, reputable rep to take you on means that you need a good track record of success or you need to have a style that they really need.
I could write multiple blog posts on reps, I will save that for later. But back to 'making it'. The two options above really are the two most obvious. As much as most artists do NOT want to be a business person, you really have to suck it up and find your inner-manager if you want to draw and paint for a living. You also need to take projects you may not find sexy and fun. And with those projects you need to do the best job imaginable. Each project is your chance to move forward, no matter how boring or dumb. I have had some stupid projects let me tell you. But, they all helped me grow in some way and were important to my business.
So, to any of you would-be illustrators trying to figure it out. Take a marketing class, take a business class, and go in knowing you will need to do it all. And if you score the world's greatest art rep, congratulations to you.