What to expect of a 3 month old
Try putting a toy in his hand. Baby will probably hold on and watch it as he moves his arm. Baby might even reach for things and grab them. He can get his hand to his mouth and suck on his fingers.
Your baby doesn't have full control over her arms and legs yet, so she may get angry or frustrated when she can't make her body do what she wants it to.
Baby likes to watch things. He will even stop nursing to follow a toy with his eyes. Hold it near and then move it away. Bring it close again or move it out of sight. Baby will continue eating. Your baby doesn't know yet that things still exist even when he can't see them.
Baby loves making noises. She can even laugh now! The more you respond to her when she "talks," the more baby will answer back and smile at you. This is good practice for real talking later.