For children's books, it's essential that you learn about designing the layout for full-color picture book. Of course, you can hire freelancers to complete the process, but I'm a DIY-er and always think it's best to understand the process before you hire it out.
Trim size. Early in the process of publishing a picture book, you must make decisions on trim size. While there are many options, I like the 8.5" x 8.5" format because it's available in paperback from both CS and IngramSpark, available in hardcover from IngramSpark, and it turns into a nice ebook. The trim size is part of the specs that you provide to the illustrator.
Templates. IngramSpark provides cover templates and sizing information for the spine with simple calculators on their site. They will email templates for the book cover, if you wish. I like to provide these to the illustrator as they work, so they know the final sizes needed for the artwork.
Artwork. Once the art is delivered, it's time to begin work. Illustrators usually use crop marks to indicate placement of the images on the page. I usually start with placing the artwork and then work on the text. If I need to do any resizing, cropping, touch-ups, etc on the art, I use Photoshop Elements, an small standalone version of the professional version of Photoshop. I ask illustrators to deliver the original photoshop files (.psd), complete with layers. That allows me to make minor changes as needed for hardcover, paperback, ebooks, audiobooks, or any other format necessary in the future. Also, be sure the art is delivered in 300 dpi, the minimum quality required by printers.
Text. Now, it's time to choose fonts and create the text on top of the illustrations. I love Robin William's book, The Non-Designer's Design & Type Book, because it taught me so much about typography and design. Take the time to work through the book and learn your options. You'll learn a lot about design! I also study current children's books to see how the design and layout is handled. It's impossible for me to advise you on which font is best for you book. I can say to avoid the cutesy and cliched fonts such as Comic Sans or Mountains of Christmas. Look for fonts that create the visual mood that's right for your book.
PDF Files. Once the book is laid out, I export a print copy as a pdf. PDF files are the actual files that you'll send to the printer. They require pdfs that fit a certain standard that makes for great printing. Currently, I export to the PDF/X-3-2002. The screen grabs below show that you can print pdfs to this standard even in Microsoft Word.
To print high quality pdfs from MSWord, Click Print, PDF, Adobe PDF. | IndieKidsBooks
On this menu, choose the PDF/X 3-2003 standard. | Indie Kids Books
Copyediting. The first thing I do with a pdf is send it to my copyeditor, and make any corrections she suggests. Then, it goes out to reviewers who take ebooks, and I print about 50 paperback Advance Reader Copies (ARC) to send to traditional reviewers and anyone else who might have interest in this book. I also send to appropriate people to ask for a blurb or comment for the publicity materials. During this time, I collect any suggested edits for a final edit.
Final Edits. About 6-8 weeks before the book's launch date, I make the final edits and upload files to all the distributors.
Resources for Layout Design
Good introductory tutorial on designing a book with Indesign. Step-by-step with lots of screenshots.
Lynda.com has many video courses on learning to use InDesign.