日、月、年 are some pretty basic kanji with readings that appear(ed) somewhat random to me. There is not only the usual distinction of 音読み and 訓 読み, but also one between the most frequent readings:
- にち： 何日、 毎日
- じつ： 同日、 近日、 先日
It seems like にち is used for referring to a particular day (what day, every day). The focus is on the day. じつ, however, seems to be used when the day is secondary and it’s more important if something is happening at the same day, soon or the other day.
- がつ： 一月、 二月、…、 12月、 何月
- げつ： 毎月、 今月、 先々月
- つき： 月見、 毎月
While がつ is used for specific months (January, February, etc.) and the oddball 何, げつ basically covers the rest. Note the Kun’Yomi reading for 毎月 and 月見. Latter is because everything involving body parts tends to use Kun’Yomi reading for some reason—not sure why, but that always reminds me of the English peculiarity of using adjectives for verbs that pertain to the senses.
- とし： 年、今年、 年上、年下
- ねん： 今年、 先年、 一年生、 学年、 光年、 小年、 去年、 青年、 ２０１５年、 来年、 新年、 年内、 年来、 年次、 年末、 年中
Basically I tend to think of とし as the “standard standalone” Kun’Yomi reading, try to remember the few compounds that use it (older, younger) and just use ねん on the rest.
Attention: Most likely this list is going to change as I learn new vocabulary.