This is a skeleton, still. You haven't defined a constructor for your Book class, and you haven't coded any of the input. In short, there's no code to "make work".
You need at least one constructor. C++ will give you a default constructor that takes no arguments, but you have no methods to set private member variables. Just for completeness, and practice, you should have a method to set every value that isn't in the constructor. So far, that is all of them.
Your main code needs a Book[] array. The assignment says "about 50" so give it 100 for now. You also need a count of how many entries in that array are used. This belongs in main.c, not in any Book method.
Book book_list[100];
int book_count = 0;
You need code to read the input text file, one line at a time, and split that into the listed fields: catalog_number, author_last_name, etc. Use these to construct exactly one Book object and store it in your array. Detect if the array is full before storing, though, and fail with an error message.
If you don't know how to split up a string into substrings, and the file contains commas separating those fields, learn. There are a number of ways and your instructor can't expect you to complete the assignment without teaching you at least one. Maybe you're expected to use multiple getline calls:
getline(infile, book_catalogue_number, ',');
getline(infile, author_last_name, ',');
...
getline(infile, availability);
Notice that each getline except the last uses a comma as a delimiter, the last uses a newline to end the "availablity" field. If your data isn't really comma-separated, then how do you handle multiple-word book titles? Pasting a few lines from your textfile could answer this...
Then you need code to sort the array. Like I said, this does NOT belong in a Book method. Book methods know about just one book (*this), and not any array or other collection of books. If you want a list of books as an object, that's another class...save that for later.
Finally, you need a loop to print out the sorted list. Again, in main.c, not in a Book method.