Being asked most people would name the twelve constellations of the zodiac and some more they have heard of or even seen (most common is surely the Big Dipper, though it is not a constellation but an asterism). In total there are 88 constellations, which can be divided into eight constellation families (see Menzel, “A Field Guide to the Stars and Planetes”). Many names we use nowadays came from the ancient Greeks. They used to assign their gods and heroes to certain figures in the sky. Due to their northern location they only gave names to those regions visible from their countries.
The regions around the celestial south pole got some of their names when the astronomer Johan Bayer made his notes about the south regions of the sky. He followed the tradition of the names of the ancient, mainly connected to the sea and its creatures. Later on the french astronomer La Caille added the last 13 to fill the star-poor regions between the existing groups. He finally broke with the traditional namegiving and used scientific equipment or instruments (there is only one exception, which is Mensa, the Table Mountain).
It should be noted that although now common, this is only the western view of the star patterns. Noone knows when mankind start giving names to stars and grouping of stars. It is most likely that constellation names were invented by early sailors for navigation purposes. But also in the deserts they might have been a good help for the people to find their ways. Therefore its quite naturally that each culture grouped the stars differently and gave them names from their natural and social enviroment.
The constellations of the zodiac we know nowadays reach back to the days of the Babylonians and Chaldeans, 2000 to 3000 years ago. Back then the sun passes through twelve constellations we still assign to the zodiac. But since these old days there have been several changes to the assignment of the stars. The sun is now passing through thirdteen constellations along the ecliptic. After the sun left Scorpius in the last week of November it moves through Ophiuchus, the Serpent Holder, in December before reaching Sagittarius, the Archer, end of December.