How can someone effectively use books like Al-Kafi for reference? When asked to find a specific reference such as Al-Kafi 1:289, does it imply volume 1 hadith 289?
This likely refers to volume 1, page 289.
Frequently, the standard Arabic printing is cited, and so you can find it in that version. If the book was written in Farsi, they may be citing a version in Farsi or with Farsi in it. So you may need to dig to find the exact narration, if they have not given publication information.
Sometimes it is easiest to try to find it by back-translating it and searching online or on library software such as ablibrary.net until you find what you are looking for. This website can also help with seaching: https://hadith.academyofislam.com/
Best wishes!