By the time your baby begins her third month, she is a lot more aware of not only the surroundings but hr own body as well. She begins to start examining her fingers and moving them around. You will notice that she is beginning to smile when she sees you, and will be able to keep her head up all by herself without any support needed for her neck. When she is lying on her stomach she will be able to hold her head up for much longer than ever before.
She will be able to hold a toy, but only if it is given to her and placed directly in her hands. You may be by now able to understand her type of cry and differentiate between them. She will wave her hands and legs much more and even more steadily rather than jerkily.
You can be a lot more expressive with your baby and she may make sounds as well. Keep encouraging her to look at her fingers and keep her on the bed under a baby gym. A baby gym will have toys hanging which she can hear, kick with her legs or push with her hands. when you are feeding her, you will find her a lot more responsive and look into her eyes while feeding. She may smile at you from time to time during her feed. She is actually communicating with you, so make silly sounds just as she is making them.
Let her take longer in the bath and allow her to kick and splash around the water. You can begin to act out nursery rhymes rather than only sing it as she is more aware of movements. Start investing in touch and feel books and allow her to feel the various textures. Encourage her to try and reach objects which are around her. She may find it difficult, but will slowly get the hang of it.
It will be a lot easier to take her out during the day as she is more aware of the environment. You can proper her up in the pram so she can look around when she visits the garden.