"Fluent in 3 months", writes that the most important thing you can do to learn a new language is to just plunge in and do it. Start speaking right away, don't worry too much about grammar, just start talking and reading and writing and after about 3 months, you should just "get it".
It works to a certain point, for Dutch. I find that, for most of my daily life's needs, my fledgling Dutch--by which I mean most things are in the right order most of the time, and that I can understand most of what most people say to me in return--is enough. I have, after all, made dentist appointments and changed insurance policies and started a business with nary a word of English. But what they say of the NT2, which I will be taking later this year (unless I don't have to, by dint of Karel and I getting married), is downright terrifying. It is terrifying for two reasons: first, it is a four-hour test spread out over two days, with separate reading, writing, listening, and speaking sections (one hour each). They really do test your comprehension: they'll write something one way in the reading section, and put the answer in another way. Ditto for listening. Secondly, they are real sticklers for grammar. This means, all your "er" need to go in the right places with the correct prepositions (actually, picking out the correct prepositions is harder than figuring out where to put "er"), verbs must be conjugated in the correct tense, with clear pronunciation of the "e" at the end of the imperfect, etc. Happily, they do not penalize for "de" and "het" mix-ups.
Like most languages spoken by a limited number of people, Dutch is a highly contextual one, where everybody knows that "bakken" means "to fry" unless it means "to bake". and "weer" means "again" until it means "the weather". The rules in Dutch are many, the exceptions are even greater. But the main reason I tend to disagree with most of what Benny has to say about taking lessons (for Dutch, at least) is that at more advanced levels, you can't really suss out the rules on your own. They aren't self-explanatory, and they certainly aren't obvious. And the sheer number of "Dutch-isms" are enough to boggle even the most dedicated immersion-type learner.
But that being said, Dutch is like any other language, in the sense that, if you worry too much about the grammar, you won't get anywhere. At some point, you just have to turn off your self-consciousness and your inner grammar marm and just start blurting things out, and trust that you'll be able to make yourself understood.