Jisho.org Forum

many words in japanese are native japanese, and many are derived from chinese. a given kanji typically has two or more pronunciations and "kun" is the pronunciation for native japanese words and "on" is the pronunciation for words derived from chinese. so typically if a word is made up of two kanji, you pronounce both characters either with the kun reading or both chararacters with the on reading. there are some exceptions, but this is probably true 95% of the time. there are also special readings not listed in the on, kun or names. (e.g., 今日＝きょう)

normally on(yomi) is written in katakana and kun(yomi) is written in hiragana.

To add to that, as a rule of thumb, use on-readings when a word is a compound of two or more kanji next to each other, and kun otherwise. This holds at least 80% of the time.

The following web page has maybe more information than you asked for, but for future reference:
http://www.sljfaq.org/afaq/kanji-pronunciation.html