The hard part is not the putting together, there are so many variations. The HARD part is thinking through the illustrations, creating a storyboard and actually getting all the sketches done.
I like to use an adhesive strip type glue, white artists tape and presentation paper that allows you to print on both sides.
So, assuming all that is done and you have the requisite 32 pages with front and back cover, you need your pages and your tools and a space to work.
( Note: in some cases the publisher will allow more than 32 pages... a multiple of 8.)
Using good presentation paper that allows you to print on both sides of the paper is a plus. It saves paper and makes a lighter product overall.
When I put a dummy together for a publisher or editor, I use only printed reproductions of the artwork. I usually print them onto a paper that allows for at least one half inch of white space at the spine edge. That area is for gluing and then taping the finished papers together.
Once I have the sketches and several finished paintings printed out I use an adhesive glue dispenser to join the back edge of each page to the next.
When all the pages and the cover are glued at the spine side in this way, I enclose the entire spine with Art Tape to hold the booklet together.
A 32 page picture book dummy will consist of two signatures, or sections of 16 pages each. In the dummy that translates to two sets of eight sheets of paper printed on both sides and joined to each other.
Since I am glueing the pages to each other at the spine and then taping over that extra edge I won't be stitching the dummy together.
Next I make a cover. The cover is simple for a dummy that I plan to mail. I use bristol board as a backing and glue the cover images to a front and back cover piece. I lay the two of these flat and leave about a 1/4 inch space between the two covers and run a strip of tape down the empty space. Then I turn it over and lay the finished dummy right on the tape.
Closing the book and leaving it closed for about an hour usually insures that the cover will stay put. I can always add some white glue if it doesn't want to hold.
I will always print out one or two finished illustrations on good presentation paper that are separate from the book.
Hopefully if the book is enjoyed the editors will have these loose images to pass around. You need to be sure all of these are labeled on the back.
I put my label on the back of the dummy,
prepare the accompanying manuscript and I am ready to present the finished work to a publisher for consideration.