If a kanji has multiple onyomi, which one do you use? Is there a rule governing this or can you use any one at any time?
There is no general rule. It depends on the compound in which the kanji appears. Sometimes even compounds have two readings.
Japanese people themselves (literate ones, that is) sometimes don't know how to read a personal name or place name.
You cannot pick just any onyomi. For instance 上 in 上手 (jouzu) must be じょう, and in 上海 (Shanhai: the Chinese city Shangai) it must be しゃん. "Shanzu" or "jouhai" doesn't make sense.
You have to recognize the compound as a word.
5Just a suggestion: this answer would be better if you used an example other than 上手, because that particular two-kanji combination can also represent うわて.– MattMay 8, 2012 at 0:21
本冊 is not a kanji compound (not in dictionary), so would it be pronounced "honsatsu", "honsaku", or "motofumi"(kunyomi)? Why?– xracMay 8, 2012 at 0:22
1or かみて ........– dainichiMay 8, 2012 at 3:04
1That particular word actually is in the dictionary (if the dictionary is big enough). It's pronounced ほんさつ and it means something like "main book", "main text", as opposed to 別冊 (べっさつ), supplementary volumes. But the general answer to the question is basically as Kaz says: it depends. e.g. In the case of 本冊, 本 seems likely to mean "main" or "this" (so almost certainly "ほん", not "もと"). 冊 is most often さつ in Japanese, so unless you have a strong reason to suspect さく or ざく (e.g. the context is tanzaku at Tanabata), ほんさつ is the most likely reading.– MattMay 8, 2012 at 5:12
+1 for useful example. When I ask my Japanese friends about this, they usually respond with "you just know." <sarcasm> This makes them amazing teachers, ya know? </sarcasm> May 9, 2012 at 9:29
The general rule is to use go-on for buddist terms, kan-on for academic terms, and so-on/too-on for zen-buddism or business terms.
Occasionally (I'm not sure how common it is) there are kanji for which the different on-readings relate to different sets of meanings.
An example is 日; in a Japanese kanji dictionary it is shown that the reading ニチ can be used for compounds in which 日 means Japan/Japanese (e.g. 日系、来日). The reading ジツ isn't used for those compounds.