How do I cite an article or book I found in the Library’s databases if it doesn’t have a DOI?

Not all scholarly journals provide a DOI and most other documents do not have a DOI (like most books or newspaper articles). In these instances, simply do not include it and treat it as you would the print version. An example of citing a journal article without a DOI would be:
 

Haddow, G., & Joseph, J. (2010). Loans, logins, and lasting the course: Academic library use and student retention. Australian Academic & Research Libraries, 41(4), 233-244.

Note that no URL or other information is included at the end and it just follows normal rules for citing a journal article. Also, according to APA Style 7th Edition, writers are not to include the name of an academic database a cited work was obtained from or include a URL back to it the work, which is why this information is not included in the above example either.