The manner in which a child acquires language is a matter long debated by linguists and child psychologists alike. The "father" of most nativist theories of language acquisition is Noam Chomsky, who brought greater attention to the innate capacity of children for learning language, which had widely been considered a purely cultural phenomenon based on imitation. Nativist linguistic theories hold that children learn through their natural ability to organize the laws of language, but cannot fully utilize this talent without the presence of other humans. This does not mean, however, that the child requires formal tutelage of any sort. Chomsky claims that children are born with a hard-wired language acquisition device (LAD) in their brains. They are born with the major principles of language in place, and with some parameters to set (such as whether sentences in the language they are to acquire must have explicit subjects). According to nativist theory, when the young child is exposed to a language her LAD makes it possible for her to set the parameters and deduce the grammatical principles, because the principles are innate.
This is still a controversial view, and many linguists and psychologists do not believe language is as innate as Chomsky argues. There are important arguments for Chomsky's view of development, however. These include the idea of universal grammar, the similarities that underlie every human language. Another argument is that without a propensity for language, human infants would be unable to learn such complete speech patterns in a natural human environment where complete sentences are the exception. This is known as the poverty of stimulus argument. Psychologists like Catherine Snow at Harvard, who study parent-child interaction, however, point out that children do not have to deduce the principles of language from impoverished and ungrammatical scraps of talk. Many studies of child directed speech or CDS have shown that speech to young children is slow, clear, grammatical, and very repetitious, rather like traditional language lessons. Social interactionists like Snow theorize that adults play an important part in children's language acquisition.
Linguist Eric Lenneberg states that the crucial period of language acquisition ends around the age of 12 years. He claims that if no language is learned before then, it can never be learned in a normal and fully functional sense. This is known as the "Critical Period Hypothesis".
An interesting example of this is the case of Genie, otherwise known as "The Wild Child". A thirteen-year-old victim of lifelong child abuse, Genie was discovered in her home on November 4th, 1970, strapped to a potty chair and wearing diapers. She appeared to be entirely without language. Her father had judged her retarded at birth and had chosen to isolate her, and so she had remained up until her discovery. It was an ideal (albeit horrifying) opportunity to test the theory that a nurturing environment could somehow make up for a total lack of language past the age of 12. Sadly, she was unable to acquire language completely. Due to this and other complications, she eventually ended up in an adult foster care home.
Detractors of the "Critical Age Hypothesis" point out that in this example and others like it (see Feral children), the child is hardly growing up in a nurturing environment, and that the lack of language accquisition in later life may be due to the results of a generally abusive environment rather than being specifically due to a lack of exposure to language.
However, there exists emerging evidence of both innateness of language and the "Critical Age Hypothesis" from the deaf population of Nicaragua. Until approximately 1986, Nicaragua had neither education nor a formalized sign language for the deaf. As Nicaraguans attempted to rectify the situation, they discovered that children past a certain age had difficulty learning any language. Additionally, the adults observed that the younger children were using gestures unknown to them to communicate with each other. They invited Judy Kegl, an American linguist from MIT, to help unravel this mystery. Kegl discovered that these children had developed their own, distinct, Nicaraguan Sign Language with its own rules of "sign-phonology" and syntax. She also discovered some 300 adults who, despite being raised in otherwise healthy environments, had never acquired language, and turned out to be incapable of learning language in any meaningful sense. While it was possible to teach vocabulary, these individuals seem to be unable to learn syntax. For further information, refer to this article from CBS, or follow this link for Google search results.
Derek Bickerton's (1981) landmark work with Hawaiian pidgin speakers studied immigrant populations where first-generation parents spoke highly-ungrammatical "pidgin English". Their children, it was found, grew up speaking a grammatically rich language -- neither English nor the broken pidgin of their parents. Furthermore, the language exhibited many of the underlying grammatical features of many other natural languages. The language became "creolized". This was taken as powerful evidence for children's innate grammar module. See Bickerton, D. (1981). Roots of language. Ann Arbor, MI: Karoma.
James Asher has put forth a trademarked term for his theories on language acquisition, TPR that could be qualified as corporal verbosity. Often used consciously in young student environments and could be considered as group modeling for older students.