Are there certain rules for knowing what role plays a radical in a kanji? I've heard sometimes one radicals tells us about how to read the kanji and other radicals tells us the meaning of the kanji but that's all I've heard, could you tell me more about this and the importance of the radicals when learning kanji?
I'll have a start at an answer, but not sure I'm able to completely answer it.
In many cases, radicals on the left side of the kanji indicate the "class" or meaning that the kanji belongs to. This seems to be moreso the case with physical objects rather than abstract concepts.
For example, 人 - person - (called "nin-ben" as the left radical): 休、体、代、伝 ([human] rest, body, generation/change, transfer). (At least one) root meaning of each of these kanji involves people (伝える has a very strong sense of "transfer information from person to person").
A better example is something like 魚 (sakana-hen). I can't think of a SINGLE kanji that has 魚 on the left side that doesn't relate to fish/ocean (look at a sushi menu).
Things in "nature" are pretty consistent: the names of trees pretty much always have ki-hen, 木. 松、柳、杉、楓、樫. (pine, willow, cedar, maple, oak). 林 means a grove of trees. From there it gets more abstract - a desk was probably traditionally made from wood, so つくえ is 机.
Once we get abstract, though, it gets messy. 心 means heart, so usually risshin-ben (when it's a line with two marks on the left) is related to emotional/feeling kanji: 慎 (prudent)、慣 (become accustomed to)、忙 (busy). Sure, we can all make the argument that one is "busy" and that affects the heart/emotion, but really, when we start making parallels like this, I start sounding more like stories from "Remembering the Kanji" as opposed to a real history of the character.
NOW, as for radicals on the right side of the kanji, they often provide the sound of the on-yomi prononciation. The kanji 官 means "official", as in like a bureaucrat (in the word 官僚). Yet, the 官 structure is part of other kanji - and takes the onyomi along with it.
The word ryokan (旅館 - Japanese inn)'s "kan" kanji includes it, as does kanri (管理, control, administer). Note that in the case of 管理, it's not on the right - it's below the radical, 竹, called take-kanmuri (kanmuri means "crown", note that it's on top, not on the left). 棺 (ひつぎ - coffin) is pronounced "kan" in onyomi (also note that it has ki-hen, because coffins are often made of wood!).
Hope this helps...
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In addition to makdad's wonderful answer, I'll add this on the issue of whether you need to pay attention to radicals when learning kanji.
This is only one data point and no more than one person's opinion, but I don't think learning radicals is all that important if you want to read Japanese. It does help to know that certain kanji (such as "heart" and "grass") get transformed into simpler versions for use as radicals, but beyond this it's more important to see complex kanji as groups of less-complex kanji, one of which may be a radical. This makes it easier to learn the meaning (if you use a mnemonic system) and the strokes (since you're not learning individual strokes, but clusters of strokes). In my case, I taught myself how to read more than 2,000 kanji without once worrying about which radical group a certain character belongs to.
The only time you might need to know the names of the radicals is when someone is trying to describe what a certain character looks like (say, over the radio) and gives the radical first. But I don't think this happens frequently enough to justify memorizing a list of radicals.