Babies change so rapidly in the first year of development, so you should expect very different things the second month than you did in the first.
The following are things for you to observe and enjoy: Your baby will eat more.
A newborn's stomach is very small, but as they age, they will eat more.
Your breasts may still be sore if you are breast-feeding, especially since babies will be suckling more.
And, since your baby's vocal cords are developing more, he or she will likely cry when hungry (or in need of a changing, or just attention).
Try to anticipate hunger and feed your child before he starts crying.
You may witness your baby's first smile.
Some babies smile in their sleep early on, but the two-month mark is where the first social smile happens.
This means that your baby will smile in response to you.
It may be something you say or a game you are playing with your baby, but he or she will smile in response to something, rather than just while dreaming.
Attachment has developed.
Many babies will grow accustomed to the attention they get from you.
They may cry when you put them down.
This is normal, and it shows that they are developing socially.
Your baby may start to hold things.
In general, your baby's hands will stay clenched during the first month.
By the second month, they will have grown enough for the fingers to relax.
You can give your child a small toy to hold; it can entertain him or her.
Black and white toys are the best, as eyes are still sensitive.
Your baby will see simply colored objects the best.
Your child may even make faces.
If you make funny faces, your child may try to imitate them.
Stimulate him or her by standing close and letting her look at your face.
This can be fun for you as well as your child.
Your child will start making noises to mimic you.
While no child will speak now, they may start to make simple sounds, like vowel sounds.
These will be more than just squeals.
During this time, you may also want to play classical music and spend time talking to your child.
The simple tunes of old songs and the sound of your voice will be stimulating.
Also, be sure to document everything with photos or video.
You will really enjoy being able to look back on these times.