When my daughter was in Junior Infants, her teacher gave to all the children in her class personalised books for Christmas. In each story, the main character had the child's name and somewhere in the story there were bits about them like their ages, best friends, etc.
The booklet was made of A4 pages folder in 4 and stapled together and had the name of a website on it, northpole.com. My daughter loved the book, and a year later, at Christmas time, we found the book and reread it. I got curious and went to the website. It has lots of Christmas related stuff, including personalised stories. To my delight, there were two more stories, and I decided to print one story for my daughter and another for my son.
There were two options on how to print the story too, one for a quick fold&staple A6 book and another option to print the story in A5 size in both sides of the paper. Which gave me the idea to try to make a properly bound book. I found a great tutorial and quickly made the two books. The one I am displaying is my daughter's - it is a bit worn out (being 3 years in a child's bookshelf), but not damaged otherwise.
Sadly the tutorial has been removed, there are other ones for single section bookbinding, but not as detailed as the one I followed. Here's one.
For the cover I used corrugated cardboard covered in patterned paper. It is a Basic Grey pattern, given free with a scrapbook magazine and printed on a thinner, shinier paper then the usual one. That's the part that got worn out. The tutorial said to use fabric for the spine, but since I hadn't any in hand I used handmade paper instead. Handmade paper is both more maleable and stronger than ordinary paper so I figured out it would do. And it did, the spine is still in good condition.
The title page and the first chaper.
Have a go, it would made a great (and unexpensive) present for any child aged 6 or under.