In modern times, there are countless ways of learning foreign languages, for example, through the Internet. But those languages are mostly well studied and understood, and a guideline on how to learn it has already been established. When I learn English, I work with dictionaries, textbooks, audio CD, etc. that are available everywhere. I wonder how the Portuguese missionaries learned Japanese without knowing anything about it beforehand; they didn't know Japanese, and they didn't have such things as textbooks or dictionaries to learn Japanese with; if anything they would have been the first people to write such textbooks and dictionaries; how did they take in totally strange words, especially those abstract concepts such as "intelligence" or "virtues"? In other words, how is an completely strange language is first learned and studied?
Here is a demonstration of a rather analytical approach to this learning about a completely foreign language when there is no common language to guide one. It is by Dan Everett, a student of Kenneth Pike, who was a master of the technique. Pike taught many students at the SIL, one of whose interests is translating the Bible into every language.
The introducer, Sally Thomason, has been editor of Language for a number of years.
Second language acquisition is closely connected to first language acquistion, so let me go a little back.
Actually, acquiring a language without explicit instruction is the natrual way to learn a language. When kids aquire their first language, no one would hand them grammar books or a dictionary either - they just learn it by constantly being exposed to spoken natural language and active interaction with their environment, and still they do pretty well.
Although this seems such a normal thing to us, it is still amazing how well children do at this enormously complexe task (there are periods in childhood with rapid growth of vocabulary, sometimes several new words each day, as well comparatively fast acquisition of rather complex syntactic constructions, and only at a very late stage, usually not until they are 5 years old, they will begin to understand pragmatic issues such as irony).
Since the mere situation of being to exposed to rather unstructered and often even false input can not satisfactorily explain how children accomplish to learn languages that well without any explicit instruction (this is also called the "poverty of the stimulus argument"), one can, I think, see some point in Chomsky's proposal of a "universal grammar" that was supposed to be interior to every human and already include all of the linguistic structure, where the individual then only has to set certain parameters in order to fully acquire a language.
Then there were theories which stated more or less the exact opposite of Chomsky's assumption, mostly behaviourism, which essentialy claimed that there is no such thing as linguistic intuition at all, but that language is just behaviour and all human behaviour is acquired by simple imitation of what the environment (for children, most importantly the parents) do.
Recent theories of language acquisition usually don't accept neither of those view in their most radical interpretation and assume both that not all grammar is already in our heads and we simply have to find out how to use it in a specific language, but that there most be some more to learning a language, but at the same time not that using language is just mimicry of what other people do too; rather, most researches assume that humans are born with some intuitive understanding of natural language which makes it possible to acquire a language without being explicitly told the rules, but that it might, to some extend, help or even be crucial to also have some active knowledge of how a language works - it must be a bit of both.
Obviously, there are quite some differences between children acquiring a languages and adults learning a second langauge.
Amongst others, children will be introuced to language in a more step-by-step way, e.g. parents teaching them simple words rather than talking to them about politics, the latter of which is more likely to happen to adults who come to a foreign country without haveing learned the language beforehand.
Additionally, there are some biological conditions which promote the ability to acquire a language in early childhood way havilier than is possible in adulthood.
Also, humans will, and in this point children and adults are not very different, learn a language in an order that is relatively universal and to some extend even very predictable.
For example, they will both start out with simple words and phrases, mostly concrete (such as "ball", "table", "go", "hungry") or very frequent ones ("Hello", "stop it"), which they than use in one-, two-, three-word sentences, building up slightly complex syntactic constructions, expanding their knowledge (which is, at the beginning, highly erroneous) to more difficult grammatical structures, more fine-grained semantic differences and eventually pragmatic, often culturally influenced subtleties.
The most apparent reason for this is simplicity: It is easier to get the connection between "ball" and someone kicking a round object than it is to fully coping with the more advanced concepts of e.g. wh-movement or passive contructions, so the former will be learned at an earlier stage than the latter.
What adds to this are practical factors: Having expert knowledge in what a language can theoretically distinguish between by making subtle changes to a sentence won't get you very far if you don't know how to use those feature because you can not even deal with the most basic vocabularly or how to form simple declarative sentences. On the other hand, people will roughly understand you if you are at least able to from three-word sentences with a vocabulary of maybe 200-1000 words, even if those sentences lack perfect grammaticality or the most powerful lexical distinctions. And you will, after some time, certainly be able to pick out some buzzwords that are frequently used and important for everyday life ("I", "you", "go", "money", "toilet"), even if you might not understand yet why the word was inflected in that very way or what that preposition expresses excactly.
This is why it is possible for humans to learn how to speak a language even if it is in total a highly complex system of lexical items, grammatic rules and pragmatic usage conditions: because they start out with the most simple and essential features and continuously expand their knowledge to more sophisticated expressions.
Despite the enormous complexity of this task, acquiring a language just by being exposed to it IS possible, this is what children do all the time, and acutally learning a language by explicitly making oneself aware of grammatical rules or meanings of words is the unnatural way to do it.
There is even a recent tendency in second language teaching design towards making second language learning more inutitive, i.e. focussing less on instruction and more on intuitive learning by hearing and using the language as it naturally occurs in everyday life, some even approach to completely do away with any explicit learning and rely solely on intuitive acquisition, as some researches argue that this is even more effective than reading grammar books and studying vocabularly lists. Fore the reasons mentioned above, this is by far not as simple for adults as it is for children, and personally I doubt I could learn a foreign language easilier by just being exposed to it; if you don't acquire it under the conditions you are in as a child learning their first language, it makes things way simpler to have some explicit knowledge about the language works, rather than having to find it out all by yourself with some vague intuition.
This doesn't prevent the general human ability though, and if you are being exposed to sufficient and qualitatively appropriate input while also being attentive to the structures it might be involved and the meanings that certain expressions might denote, then it is indeed possible to acquire a langueage (rather than actively learning it) just by hearing and using it, even if you have never known those constructions before; simply because the human brain is made to understand language without actively being aware of specific grammar rules or word-meaning relations - in fact, this is even the more normal way to do it.