I need a book for my teaching and/or research, but my university's library doesn't have this book. I don't think I'll use it enough to justify spending money out of my own pocket to own it. What other ways should I try? I searched Internet, there is no "free" (in whatever sense) PDF of it either.
Ask your university librarian.
Usually universities libraries collaborate with each other. They can look whether the other universities have the book (I know this happens within Canadian universities)..
Usually I try to
Aks to profs. at the university. Most are happy to lend them for a short time.
Public libraries can be nice, but for some scientific literature I must admit they are not optimal
A somewhat grey area is buying them used books online. A online interface to physical 'used books' shops is use often is abebooks.com. Buying them a tenth of the price with shipping from Asia most of the time in comparison to the price at the university bookstore does feel like cheating but meh.
The last option could become illegal in the US depending of this court case, but for now it seems legit.