The point about first language acquisition is that it is done fairly quickly without (normally) relying on teaching grammar. By the time a child turns four he has mastered the majority of the grammar he will ever learn. I have a four year old son who speaks nearly flawless English within his vocabulary limits. Since he didn't really talk for the first year, that amounts to just three years of active language learning.

I have to disagree with the notion that learning grammar from a reference book is faster than other methods. One can look up grammar points in a reference, but that isn't the same as learning. By contrast, there are some phrases and sentences I memorized early on in Russian which I can always recall easily which illustrate various grammatical constructions.

If you are interested in learning more about these things, get some of the work done by James Asher or Stephen Krashen or Rod Ellis. Each of them are experts on language acquisition, and each takes a different approach, but NONE of them promotes the old grammar-translation method. I've found Asher's work in particular to be particularly helpful when I'm teaching.