This is by either covert, where the observer does not interact with the child, or children, being studied. Or by overt observation, where some interaction with the child, takes place.

Many studies have been done on children ranging from birth to teens. Look in any child development book (Carolyn Meggitt has written a few) and it will tell you the developmental stages that a child should go through eg: a baby will coo and gurgle...this is one of the first stages of speech/communication. Many psychologists have studied children of all ages to ascertain how they develop and at what rate etc eg: Jerome Bruner and Jean Piaget to name but a few. As a nanny i make observations on the child i care for to find out all sorts of things eg: how his speech is developing. Jack is 19 months old so still learning to speak but he already has a massive vocabulary. I carry out observations in various ways...timed/event samples, participative...there are various ways and each one is best suited to certain types of investigations.