First you need to start with your manuscript and this usually takes time.
You need to write, and rewrite. You need to aim your story to your target audience and make sure you are writing appropriate for them. You have to try to find a story that is unique and not told already since the market is so tough right now.
Editors are always looking for something fresh and new. Try to tell a fun story and not something that will teach kids a lesson. Always try to make the main character, be a kid or animal in the book, solve the problem on his own. If it's a picture book you might need to cut a lot of your text since most picture books have a few words. The less text the better.
When you feel your manuscript is perfect, then you need to ask yourself if you really are a great artist. I'm sorry to say, but if you are not, then you have far better chances of getting your story picked up by a publisher if you submit ONLY the manuscript.
Professional artists or talented people that really know how to draw can get away with trying to submit a story with illustrations. If you feel you belong to this group, then you need to work on a dummy. A dummy is rough book made by yourself, it can be very simple. Actually I suggest to try and keep it very simple. Just have the pages folded and stapled in the middle to make it look like a book. Then you submit it with sketches and the text in place. Do not try to make each page with a finished color illustration. This will take you a lot of time that will end up being a waste of time because chances are that the book will need editing. So just fill those pages with sketches and just have one spread (2 facing pages) with a finished illustration and maybe the cover too, if you feel like it. That ways editors can have an idea of how the book would look once it's finished. There is a lot of information on the web regarding dummies. Make sure to take advantage of this.
After all of this, you need to sit down and do a lot of research. The more the better. Look at publisher's websites. See what books they print. Look in bookstores and see what books are out there and what publishers prints book that your think are similar to yours, not in story but the type and feel of the book.
When you have some names narrowed down you have to see which of those publisher accept unsolicited manuscripts. What this means is they are willing to see your story without and agent sending it to them. If you have some names that fill this requirement then you can send your dummy to them. Always read their submission policy and make sure to follow everything they say. They receive tons of submissions and they tend to be very strict on these things.
You could also try to go the agent route and send your dummy to an agent first. If an agent likes it, they might ask to see more of your work and might be willing to represent you. The agent then submits your story for you to all those mayor houses that are impossible to submit on your own. Agents take cuts from your work of course and they will handle contracts, try to get you the best fee, etc..
Since you mentioned you passion for art, maybe you can try your route to getting published by being an illustrator first. For this you need to create a portfolio with 10 or more really great pieces that show you can draw kids and animals in different settings and display all kinds of emotions.
Make sure to have a website showing your work and then you can send postcards to publishers with your information and a link to your online websites. If they like your work for a particular manuscript they may hire you to illustrate it.
All this requires a lot of time and effort and getting published is not easy but it's not impossible either. If this is your dream, you need to keep at it. Work hard and don't give up.