Hmm, to answer your main question about the difference between Onyomi and Kunyomi, here it is=>
"The kunyomi is the Japanese reading of the kanji. The Onyomi is the Chinese reading of the kanji.
When multiple kanji appear in the same word it's typically read with the onyomi pronunciations, and typically when kanji appear as a single kanji in a word it's read as kunyomi."
---->this answer is taken from here=>
http://www.japanesepod101.com/forum/viewtopic.php?t=2408
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I agree with Makoto-san that the more you learn Kanji, the more you are able to get the hang of when to use which pronunciation of the same Kanji. As of now, I memorized probably about 50-60 Kanji and for me it's almost predictable to understand when to use which pronunciation.
For example the Japanese for Sunday is 日曜日(nichiyobi). There are two 日 in this word but the first one is にち and the last one is び (not ひ). So, you can now understand that the days of week always use the same pattern as in English (i.e. the "day" in Sunday, Monday, Tuesday...etc are always said び in Japanese).
Another nice example is the word 月. As far as I know/learnt, there are three pronunciations of this word with three meanings:
1. 月(がつ)=>month
2. 月(げつ)=>month (as in the Japanese for Monday=>月曜日 [getsuyobi])
3. 月(つき)=>moon
I hope I was able to help you a little bit through my answer/explanations!
^_^