There are some very loose patterns as you’ve noticed, especially with 月 and 日 about which reading is used when you’re talking about months vs talking about the moon, for example. Other than that you’ll just need to trust memory and repetition to teach you which reading is used in which context. Much in the same way we’re required to learn homophones and homographs in English by familiarity.
I can’t really put it much better than this: