That question is something that has been confusing me for a long time when I started learning Japanese. :-) My current approach is: There are basically two kinds of words, "native Japanese" words and "Chinese-style" words. They also differ phonologically. For native Japanese words, the beginning of the word or even the whole word (mostly for nouns) is replaced by a Kanji. This Kanji is purely assigned by meaning, and if one word can have different meanings or shades of meanings, one can use different Kanji. Sometimes multiple Kanji are used for one word, as in 今日 "kyou". That means you need to know the word, or you can't pronounce it. If you know the Kanji, you may guess the meaning, but you still can't pronounce it. Chinese-style words work like foreign words of Latin or Greek origin in western languages ("biology" etc.). They consist of parts with seperate meanings, and if you know the ON-pronounciation, you can read them. Sometimes there are several ON-pronounciations, then again you need to know the word. (Though I suspect euphony may play a role, too; I have been able to guess correctly in some cases, but I'm not sure if there is a rule). But Names are totally wild, Kanji used for names can have even more pronounciations. So, bottom line: Learn the WORDS together with the Kanji. For native Japanese words, learn the Kanji that can be used with them. For the Kanji, learn the meaning and the ON-pronounication (you'll learn the KUN-pronounciation when you learn the respective word). At least for me, this seems to work well enough.

Most kanjis have at least two readings. Which one to use is a matter of familiarisation with the language. You can't learn rules here. You will get used to it as you progress. It gets quite obvious with time, so be patient.