As a published children's book illustrator, I often get asked the question, "How do you break into the industry?" from other earnest and extremely talented artists. While I can't describe the journey in only one post, I can start by recommending a few books that have more than earned their space on my bookshelf. Pick these up at your local bookstore and you'll see what I mean.

#1: Starting Your Career as a Freelance Illustrator or Graphic Designer.
I discovered this book some time after graduating from the Rhode Island School of Design, and it covers many things I had learned there (how to build a portfolio, design your logo/brand identity, etc.) while giving additional insight for things that one can only learn in the real world (all of the legal and tax considerations that no artist wants to think about). I'd say this book is a must for greenhorns as it gives a realistic overview of how to get started. It also offers "Professional Viewpoints" in the form of quotes from successful freelancers, and an entire chapter of forms and charts templates to assist you in designing your own.

#2: GAG's Handbook of Pricing and Ethical Guidelines.
To try to describe the entirety of this book in my own words could never do it justice; it is quite literally considered a Bible for professionals in the industries of illustration, design, and animation. The Graphic Artist's Guild (GAG) comes out with new editions regularly as industry standards change, and it is a pricey book, so keep that in mind when purchasing.

#3: Children's Writers and Illustrators Market.
This book is absolutely necessary when you want to build a mailing list for promoting yourself. Within these pages you'll find thousands of directory listings for publishers, editors, art directors, and agents who want your work. The entries for each listing include contact information, the genre they're interested in, query guidelines, payment terms and tips. A new version is printed every year (folks in publishing move around A LOT), so the information is nearly always fresh. I recommend you spend some time with the newest edition courtesy of your local library if you cannot afford one or don't want to purchase a new version every year (check the reference section, you may not be able to borrow the book depending on your library).
While these books are certainly not the "be-all, end-all" for information on the publishing industry, they're excellent places to start. I'd welcome other book recommendations, too, so please feel free to post links in the comments. Thanks for reading!