How to count the number of instances of each foreign-key ID in a table?

Your query is almost right and it’s the right way to do that (and the most efficient)

SELECT books.*, count(orders.book_id) as number_of_orders        
from books
left join orders
on (books.book_id = orders.book_id)
group by
    books.book_id

COUNT(*) could include NULL values in the count because it counts all the rows, while COUNT(orders.book_id) does not because it ignores NULL values in the given field.