Babies communicate in a variety of ways from the moment they are born.
The youngest of babies will connect with his parents both by crying and by making eye contact. This most primitive of exchanges enables a baby to express his needs or displeasure and also allows him to bond with his parents. As a baby gets older, his methods of communication become more sophisticated. He graduates to coos and smiles to express his contentment, and his cries become distinctive to his needs. At this time, he is probably discovering the many amazing things that he can do with his hands. This skill will come in handy soon.
Even though a baby as young as two months has probably already discovered his hands, he is not yet quite ready to sign. Although it is fine to demonstrate signs at any age, a baby this young does not have the dexterity to sign, nor is he able to make connections between an object and its sign.
When a baby nears toddlerhood, his growing independence makes him work harder to get his point across. It is important to him that he is able to express himself, and it is equally important that you respond appropriately. He will begin to be more adamant with his verbal sounds and babbles and will begin to gesture with his hands. Commonly, he will point to things that he wants or raise his arms to be picked up.