The first option on the list, "buy one of the rare copies on the market", is not as simple as it sounds, because finding an antiquarian bookseller that still has a copy of the book is the most challenging part of finding the book.
Depending on where you live, you need to find a way to identify sellers that might have the book. For example, if you live in the European Union and you can deal with a German user interface, Buchfreund.de is a good place to start. The site offers a federated catalogue of antiquarian booksellers in Germany, Austria, Switzerland, the Netherlands, the Czech Republic and Hungary (and possibly a few other countries that I have not yet come across in my searches). Since the largest share of booksellers represented on Buchfreund.de, the majority of books are in German. However, I have been able to find many academic titles in English that had been removed from university libraries. You can also search for antiquarian or out-of-print books at ZVAB - Zentrales Verzeichnis Antiquarischer Bücher (literally "central registry of antiquarian books").
If the book you are looking for is an academic publication, you may find it on sites specialising in that types of books, such as Studibuch in Germany.
If you can handle a French user interface, Chapitre.com may be a good alternative. According to Livre à Paris, Chapitre.com is an online bookseller specialising in antiquarian and out-of-print books, with a catalogue of over nine million items. In France Place des Libraires also allows searches over many book sellers; most books offered here are new but with some luck you can find an out-of-print book.
(The article Acheter un livre ancien, épuisé, rare ou indisponible also also mentions Abebooks, Amazon and Price Minister as sites where you can find out-of-print books, but these are sites which many people are already familiar with.)
Without those specialised sites and federated catalogues, you'll need to contact individual antiquarian booksellers, such as Skulima in Germany (academic titles). The post Les bonnes adresses de bouquinistes et librairies provides lists for antiquarian booksellers in France (mostly), Belgium, Quebec and Ireland. Leslibraires.fr provides a map of booksellers in France and tells you whether the specialise in new books or out-of-print ones. (If you live in Paris, you can also visit the famous Bouquinistes, but that is not a very efficient method.) You can also use the directory of the Independent Online Booksellers Association or check the list of booksellers' associations on Wikipedia.
Another big search engine for used and rare books is BookFinder, which appears to work like a meta search engine, since it provides results from sites such as Buchfreunde.de, ZVAB, Amazon, Alibris etc. This allows you to compare prices from different sellers and marketplaces. This is worth doing, since prices for out-of-print books can vary considerably.