By the third month your baby will grow increasingly aware of the outside world, and settle into his or her own routines. Movements such as kicking and waving reflect your child’s excitement.

As their vision improves, babies become fascinated with their hands. At this stage, they may start to make intentional movements towards objects that catch their attention. You can also expect to hear lots of baby sounds. To encourage language development, it’s a good idea to actually engage in this "baby talk" with your infant.
Safety checks for the third and fourth months:

• Your baby’s increased activity means you have to be even more attentive. Never lay the baby down on a couch or bed; instead place the baby on the floor when he or she wants to move around.
• Never leave your baby alone with other children or pets.
• Be especially ‘toy wise.’ Before buying a toy ask yourself: Is it safe? Appropriate for my baby’s age? Stimulating?