When embarking on your journey as an author or illustrator, you will want to pitch your work to the right publisher or to the right agent. This takes time to practice your craft and research which topics are a good fit for your genre. You can learn more about how to practice you writing and illustration skills with the books list from this blog.
Once you have your work ready to send out, you will need to research which publisher is the best fit for your book. Visit your local bookstore or library to see what is currently being offered. The books you grew up reading are different than the books on the market now. Visit the Publishers Weekly to research which house or agent is the best fit for you. SCBWI has a publication called THE BOOK, which has loads of useful information for members, as well. Another source book is the CHILDREN'S WRITERS & ILLUSTRATOR MARKET.
I should also mention self-publishing. With this route you can choose to pay for a fully assisted publishing service. The cost varies depending on the services offered and can be beneficial for those who have no desire to handle the business side. The Author receives better royalties than a traditional publisher contract. However, with the following Do-It-Yourself options you may earn more: EBooks-only Publishing Services such as wattpad.com, Print-on-Demand (POD) Services or Traditional Print Runs.
For more details on the different paths to publication, Jane Friedman, CEO and Co-Founder of Open Road Integrated Media has created a very helpful info graphic that you can link to here.