Q. How do I find a book's digital object identifier?

I'm assuming that you are trying to create a citation in APA style which now asks for DOIs (Digital Object Identifiers), when available, for electronic materials.

You would only need the DOI if the item is in electronic form.  If it is, the DOI should be displayed somewhere on the title page of the book or in the first few pages of the material.

Not all electronic materials willl have a DOI.  This is a voluntary system that publishers (particularly of journals) are using to help readers locate electronic content.  They use it in place of a URL (Uniform Resource Locater) because URLs usually include a web address of a particular machine or web site.  These addresses can change and frequently do.  When using a DOI, the publisher registers with the DOI issuing system so that if the web address of the material changes, the pointer from the DOI system can be changed.  Not all publishers register, so there may not be a DOI available for the material you are looking at.  In that case, you will not be able to list one in your APA citation.

Of course, you would not find a DOI for a physical book or article, so you would never include such a number in a citation for that type of material.