Introduction to Psychology/Language and Cognition
Basis of Language 
On its most basic level, language is composed of phonemes, the smallest units of sound that are distinctive for speakers of a particular language. There are roughly 40 phonemes in english (ph, ah, etc.). In basically infinite possibilities, these phonemes combine to form morphemes, the smallest meaningful units of language. Morphemes are typically word roots, prefixes, and suffixes. Morphemes combine in infinite numbers to create words, which are arranged to create sentences (syntax) according to the rules of semantics.
Stages of Language Development 
When a baby is born, her trachea is unable to produce articulated sounds beyond a high, unclear cry. As the baby matures, the trachea sinks lower and lower, enabling the baby to begin articulating words. At this point, which happens about three months after birth and lasts about two months, the baby is said to be in the "babbling stage" of language development, in which she will babble nonsensically. She has not yet narrowed her vocabulary of phonemes, and thus is in one of the "critical periods" of language development in which all phonemes are equally developable. After a point, the baby exits the babbling stage, having attained a basic understanding of the phonemes in her language. Having left this stage, she begins to attempt articulating words in her parents' language, thus entering the "household language" phase of development. This stage is characterized by a language that is not necessarily the baby's parents' language, but which does follow rules and a basic syntax. Words like "wawa" to represent water and "dada" to represent dad emerge in this stage.
At around age one, most children enter the "one-word stage" of development. In this stage, the baby begins to speak in words of the parents' language, usually after positive and negative reinforcement from the parents during the "household" stage of development. The baby speaks in single words, and may communicate ideas using body language. For example, a hungry baby may say "milk" and point at her mother.
Beginning around age two, the child begins to form basic two-word sentences in what is said to be the "two-word stage" of development. Basic sentences like "johnny hungry" are common. Closely following this stage, the child enters a stage of "telegraphic speech" in which speech is much like that of an old telegraph; "joey hungry! want food!" is an example of this type of speech.
After the child reaches telegraphic speech, language develops quickly. Grammar and syntax quickly become apparent in the child's speech, and his/her vocabulary grows at a rate of about 40 words a day. As the child reaches adolescence, his/her ability to learn vocabulary at this quick pace passes, and he/she is said to be out of the critical period for learning language.
Nature-Nurture in Language Development 
The way language is actually learned is a hotly debated topic. Behaviorist B.F. Skinner introduced in 1957 the idea that language is learned as any other behavior is learned: through reinforcement and punishment. Around the same time, Noam Chomsky introduced the idea of "universal grammar," an inborn understanding of syntax passed on in the actual genetic material of humans. Strong evidence exists on both sides of the debate; numerous case studies have been done, yet no conclusions have yet been made on the topic.
The Linguistic Relativity Hypothesis 
Linguist Benjamin Lee Whorf introduced in 1956 his "linguistic relativity hypothesis." The basic idea of this is that a person's language directly influences his or her cognition. That is language determines the way we think.