Teaching young children about authors and illustrators through author studies or author adventures is good. Letting them become authors and illustrators is powerful!
In my first year as a classroom teacher (so many moons ago!) publishing student books meant having students use crayons/markers/colored pencils to draw out the illustrations and hand-write the content for each page, then physically binding them with either tape, metal clip rings, or those plastic comb things that tended to pop up in your face if you didn't get them positioned juuuust right. :)
Not that that isn't also a good option for publishing student work today!!! After all, the authorship process is basically the same no matter what tool you use. At the end of the day, publishing is publishing.
There are a few of the many services available that can take some of that labor off your hands and also provide your students with a polished, professionally-bound copy of their work that they would truly cherish for years to come. These are listed in no particular order, and no one is receiving any compensation whatsoever for their mention. They seem very useful resources for use in a collaborative lesson in with classroom teachers or as an ongoing project in the computer lab. They will have their own respective planning tools to use in creating student work, as will be the payment process. Talk to your local school officials and financial record keepers about how to make these work for you!