I spend a lot of time in libraries. Perhaps the following summmary will help with the confusion you've experienced in the material you found online. Massive amounts of information is overwhelming. Hope the following helps you out. Good luck on Friday.
Physically Finding Library Materials
Libraries—school, public or government—classify materials (books) according to
either the Dewey decimal classification (DDC) or the Library of Congress Classification (LCC).
Along with the essential information in an online catalogue each book is assigned a code
(numbers, letters, or a combination). Determine which system the individual library uses
to classify its collection. There are reference books (in the reference section) that set out the various divisions of both the DDC and LCC systems. Or Google “Dewey decimal
system” or “library of congress system”.
Most shelves of books and materials in a library are numbered with a range (eg. 745.25- 746.95). Some even have signs stating sections (eg. biography, technology,). Say the book you’re looking for has the number 813.52. Find the shelf of books with the range
812.75-813.95. Search for “813.52” and you have found your book “Critical Essays on
Steinbeck’s the Grapes of Wrath”. Fiction collections are shelved alphabetically by author.
Adding material is easy. Some codes have 5 or 6 decimal places. The new book is coded
consecutively in its section with the next available number.
Note: I am familiar with DDC and therefore used that system’s coding for my example.
Same process tho’ in a library using LCC; learn (or look up) the divisions and
match the code with an area of shelves and voila the book.
Note 2: In your case, check the DDC or LLC on the book you PUT ON
(as opposed to TAKE OFF) the shelf; locate the area (as above)
and shelve the material.