Babies are born with no coordination or motor skills at all. Motor skills and coordination begin to develop about a month after birth. The baby will learn to control his eye movements and hold his head up. Those are the beginning of the development of motor skills. Motor skills must be accompanied with coordination in order for the child to learn to crawl, walk, run, etc.
So how does coordination develop? When a baby is about three months old, his coordination has developed to the point that he can intentionally bring an object to his mouth with his hands. By the time an infant is six months old, he can transfer objects from one hand to the other. His coordination is developing.
At some point before a baby is nine months old, his fine motor skills begin to develop, and his coordination becomes more advanced. He can pick up a small object using his thumb and first finger.
By the time the baby is about one year old, he will have mastered many of the coordination movements that allow him to sit alone, crawl, walk (maybe), etc. His fine motor skills develop much more slowly, but he might be able to scribble with a crayon or a pencil.
By the time a child is two years old, his gross motor skills and coordination are becoming well developed. He can climb. He can jump lifting both feet simultaneously, etc. Fine motor skills and coordination are also becoming better developed, but still lag behind gross motor skills.
Motor skills and coordination continue to develop, and by the time a child is six years old he can hop, skip, jump, and throw and catch a ball. Most children can tie their own shoes and button buttons and zip zippers as well.