newborn
Newborn infants arrive in the world having already learned many speech and language lessons. Babies in the uterus hear and respond to familiar voices. They prefer human voices over other sounds, and prefer the sound of his or her's mother's voice most of all. Also, newborns can recognize whether sounds are part of his or her native language.

1 month
At one month, babies are soaking up language skills through interaction with the people around them. Babies respond well to motherese, or "baby talk," which is a higher-pitched, slower speech with emphasis placed on alternating words. Most parents instinctively speak this way to their newborn, gradually incorporating normal speech patterns and pitch.
If you have a broadband Internet connection or a dial up and lots of patience, check out this excellent short PBS video about parent/child communication.
A one-month-old baby is already building what linguists call language competence (what a person knows about a language) which is a prerequisite for language performance (how well a person can use a language). Babies language performance isn't much at this pointjust small throaty sounds and gurglings.

2 months
At two months, infants continue to learn language by listening to the basic and distinct sounds (phonemes) of the language they hear. They can already start making grunting vowels sounds. Vowels sounds likely come before consonants because they are easier to produce and require less coordination of the tongue.

3 months
At three months, babies begin to whimper and to make glottal sounds as they continue to experiment with making sounds. As we touched on above when we discussed the sounds waves of sentences, at this stage babies are also paying close attention to learning the melody of a languagethe rhythm of sounds and pauses, the varying pitch in the voice, and the patterns of loudness and softness.
In linguistics, a language's musicality is called prosody.

4 months
At four months, babies begin to babble. Babbling is big stuff to a linguist (and a parent), because in linguistics babbling is a critcal early stage of speech development, not mere "meaningless gobbledygook."
One way linguists differentiate between a baby's babbling and non-speech sounds
is by watching the baby's mouth. If the baby has more activity on the right side of his or her mouth, it is an indicator of heightened left-brained, linguistic cognition.

5 months
At five months, a baby is trying out a lot of new speech sounds. Many of the new sounds are attempted somewhere between contentment and crying. The typical pattern is this: a baby makes happy non-speech sounds of contentment, then he or she gets a little more fussy and uses more speech sounds, then he or she starts crying.
Five-month-olds begin to watch and imitate adult's mouths to practice the mechanics of speech sounds. Some precocious five-month-olds utter his or her first word, and it's no surprise that a common first word is "ma." The word "ma" is composed of the bilabial consonant [m], which is easier for a baby to "see" as he or she watches and imitates an adult's mouth, and the mid-central vowel schwa, [ə], which doesn't require any complicate coordination of the tongue and lips.

6 months
At six months, babies will still listen just as long to a foreign language as to their native language, but this ability starts to fade during the next few months of the baby's development. Ultimately, a baby who is not frequently exposed to another language will stop hearing non-native language phonemes and consider them non-speech sounds.
If you have a baby and want him or her to develop fluency in a second language, it is helpful to expose the child to the sounds of the second language by six months of age and frequently thereafter.

7 months
At seven months, an infant is becoming more adept at manipulating his or her vocal tract and can make several sounds in one breath.
Seven-month-olds start to recognize the meaning of common words such as "mama"they may speak "mama" earlier, but most babies don't attach a meaning to words until this stage. A seven-month-old will more frequently use speech or non-crying sounds to attract and keep a parent's attention.

8 months
At eight months, a baby's head will move toward noise. The baby will start turning his or her head or look up with recognition when someone says his or her name. The baby will also start responding to one-step commands like "come here" and "no."

9 months
At nine months, a baby enters the one-word, holophrastic stage. At this stage, a infant will start using single words to convey complex ideas. For example, a nine-month-old might speak the word "dada" like "DA-DA!", meaning "I'm so happy, my daddy's home!" and "Daa-dA?" when they are asking "Is my daddy here?".
Nine-month-olds can do this because they are beginning to learn where to put the stress on the simple syllables they can articulate.

10 months
At ten months, an infant starts to wave "bye-bye" and shake their head "no."
A ten-month-old will also know what relatively complicated phrases like "it is time for your bath" mean, even if they don't know what the individual words mean. Through repetition of the event, they can attach meaning to the phrase.

11 months
At eleven months, infants start to group things into classes. Broad measures like shape, color, and size seem to be of the utmost importantance to infants at this stage of language development, and they will over-generalize because of it. For example, if at this stage you teach your infant the word "dog," they will likely call your cat by the same name for a while.

12 months
At twelve months, most babies start to walk. They also enter the telegraph stage of their language acquisition, characterized by the use of a 2-8 word vocabulary. A couple of these words can be put together to make short sentences like "daddy bye-bye" and "you mommy."

13 months
At thirteen months, infants start to point, which is an important part of learning language. When infants point to something, it is usually not because they want you to bring them the object, but because they want you to teach them the name for the object.
Watch this short video for an example of the importance of pointing in an infant's language development.
Windows Media movie [best for most PCs] :: 2 MB download
MPEG movie [another format] :: 3.5 MB download

14 months
At fourteen months, infants start to enjoy reading time. Books with lots of pictures and books with lots of repetition and rhyme (i.e., Dr. Seuss) are always a popular choice. These books help start teaching infants the grammatical rules of syntax.

15 months
At fifteen months, an infant starts to recognize the names for his or her body parts. They can also combine the ability to point with the ability to match a word to its origination. For example, if asked "where's the kitty cat?" the infant can combine those skills to point toward the cat.

16 months
At sixteen months, an infant has a speech vocabulary of 6-8 words that they can articulate almost as fluently as an adult. At this stage, infants can put together short sentences of function words like "Mommy kissy boo-boo" or "Daddy go sleepy."

17 months
At seventeen months, an infant can understand a lot of words they cannot pronounce, perhaps as many as 40-50. The abilities of their minds are forging ahead of the compententcy of their vocal tracts.
At this stage, infants can also use words to express emotional needs like "up mommy!" to be picked up, held, and comforted.

18 months
At eighteen months, an infant becomes a toddler. One of the reasons a toddler is defined as eighteen months old or older is because at this stage the child enters a period of explosive language development.
At eighteen months, toddlers can understand sentences as long as seven or eight words and they can tell if those sentences are grammatically correct. For example, they know that a verb ending in -ing needs a form of "to be" preceding it.
Up to this point, most children have been learning the meaning of approximately one word every three days. Suddenly, they begin learning about 10-12 words a day, every day. By kindergarten many children know the meaning of 10,000 words, although they cannot pronounce them all and probably can write and read only a handful of them.
By the time he or she graduates from high school, a person will probably have a 30,000-60,000 word vocabulary.