So, now you're home with this little bundle! Ideally, it would be nice to have some quiet time for a few days to settle in with your partner and the little one. More likely, there will be a lot of excitement, with phone calls & visitors. It may be a while before you actually get to see what this new family is like. It may take some time to absorb the fact that you are a father and to decide what that means for you.
If you were able to be involved in many aspects of the pregnancy and delivery, now is the time to stay involved. Even if your role seemed to be on the sidelines during pregnancy and delivery, there are many reasons now for you to be a big part of your child's life.
There are many good resources for fathers that give information about how to take on this new role.