Understanding Kanji

I'm leaning the Japanese language at my own paste. It seems pretty straight forward. The only thing bothering me about the Kanji are the Kun-yomi and On-yomi reading. I'm not entirely sure on what they mean. Am I supposed to read certain ones for a certain Kanji? I hear that On-yomi is the chinese reading. Does that mean I should only read the Kun-yomi when speaking or reading a kanji in Japanese?

No, I'm sorry to say that Japanese use both yomi properly, even at the same time.
On-yomi is derived from Chinese pronunciation but it's not Chinese.

For example, about 朝晩(asaban; day and night), 朝(asa) is kun-yomi and 晩(ban) is on-yomi.
In the first place, about 音読み(on-yomi), 音(on) is on-yomi and 読み(yomi) is kun-yomi.

You have to learn both.

Generally(not always), from what I've seen, kun-yomi is for single kanji with or without their accompanying okurigana, and on-yumi is for words with multiple kanji. This obviously doesn't apply to names though. Though I only know a few hundred kanji, so I'm no expert on this.

When you hear that on-yomi is the "Chinese reading" it just means that it was derived from Chinese historically. You need to learn the reading for each word you learn, whether on-yomi or kun-yomi. Some kanji have more than two readings! 生 is one example, it can be read in a number of ways depending on the word it is used in.

As everyone else has said, you can't ignore the on-yomi, as they are widely used for different words. I would suggest that you learn vocabulary for new Kanji as well as learning the readings. Although the rule is that the on-yomi is used for compound words, and kun-yomi for non-compound words, there are many exceptions, likely around 30-40% of the vocabulary. Many Kanji also have multiple on-yomi or kun-yomi, or have special readings used only for 1 word, so it can be difficult to read some words correctly if you haven't previously studied them.

I think I should also add that although it is better to learn all readings, often some readings are more important than others. Sometimes even the kun-yomi may be very rarely used, and it won't be a problem if you forget it. For example もち。いる the kun-yomi for 用 is very rarely used. Instead people generally use the compound words 使用する or　利用する, or use 使う.

Okay cool. Thanks for the feedback. Its just the separation that's bothering me. I understand they show which came from Chinese, but having them in multiple sections is very confusing. :P