I'd start with the difference between fiction and non-fiction, and how books are arranged in a particular way so that it's easier to find them and the information in them.
You could explain the difference between the contents page and an index - the contents shows how the information or story is arranged in the book in chapters or sections while an index in a NF book shows you how to find the pages which have information on a particular subject or thing - which may be on several different pages or in different chapters.
Are the fiction books arranged in any particular way? Eg by author, or by reading level? If not, I'd concentrate for the moment on the NF (while trying to persuade someone to do some organisation!)and explain the categories.
Do you know what the categories are? Many school libraries use categories based on the Dewey decimal system, with colours roughly corresponding to one or two 'hundreds'
Ours is: Black 000-199: general information, encyclopedias etc
Silver: 200-299: religions
Yellow: 300-379: society and its organisation (includes books about towns, recycling and the environment, police & emergency services, shops and education
Brown:380-399:travel, customs and celebrations
Orange: 400-499: languages including dictionaries
Red: 500-569: science including Maths, so would have books about light, sound, water, electricity etc, also includes geology, so has books about earthquakes & volcanoes
Dark green: 570-599: nature including dinosaurs, habitats, animals (though pets usually go with farming!), birds, plants etc
White: 600-629: technology including medicine, the human body, computers and robots, cars
Light blue: 630-699: products, farming, which includes gardening, pets, food & cooking, materials, eg wood, brick, paper etc
Pink: 700-799: art, craft & leisure, includes architecture, so books about buildings are here, also hobbies and sport, plus film and TV
Purple: 800-899 literature, so plays and poetry might be kept here
Light green: 900-919: geography/travel, including atlases, books about various countries
Gold: 920-929: biography, heraldry and flags
Dark blue: 930-999 history
Yours may be different but try to sort out what subjects are in each colour section is there a list? It can help if you can see where the books about their current theme/science subject are and use that as an example, or if the fiction is reasonably well organised, see if they can work out where the book they are reading in class would be kept.