This diversity is by turns intriguing and frustrating. The good news is that to start off with, you really don't need to know all the readings for the more versatile kanji. Again, you should consult with your teacher over what is likely to come up in any test you're thinking of taking. This is a kanji site, not a vocabulary primer, so forgive me if I stray from the JLPT wordlists occasionally.

Anyway, plenty of kanji have only one particularly common meaning, and as a result can be easier to pick up than you might think. Anyone who has been in Japan for as little as a week ought to be able to recognize yen, entrance, exit, month, day and the name of their nearest train station, for instance.

In addition, it's often easier to remember the meaning of a kanji than the exact pronunciation - which may be all you need. And once you've learned a kanji, you mysteriously start seeing it almost everywhere you look... funny, that... which is great for practice.