A Baptism is a water purification ritual practiced by a few different religions, Christianity, Mandaeanism, and Sikhism to name a few. Its origins are Jewish however, from the ritual of mikvah.
The most popular version of a baptism is in the Christian religion, the idea is to clean the person of sins, and to unite the person with Christ. It both symbolizes new life (which is why babies often get baptised) and it also establishes a person within the religion.
The general term baptism often refers to a new beginning, the phrase "baptism by fire" means to be welcomed into something in an unpleasant manner. When I hear that phrase it makes me think of war heroes fighting their first battle. After that battle they are not rookies, but the "baptism" was not gentle.
The process in the Christian religion is to sprinkle some water on the head of the child (or adult as the case may be). The priest will say a few words of importance while he is baptising the child (or adult), but I don't think there is one set thing to say, the act of putting the water on the person is the key element. It's always nice to have something nice to say at these sorts of things.
This site may help you.
http://www.americancatholic.org/Features/Sacraments/Baptism.asp
