Of course I am not going so far and saying that the fathers should get into that zone but here are some ways dad can help breastfeeding!
Breast feeding is a long and tiring process and many times the mom will feel like giving up. Encourage and support her to continue. Be present spend time with her. Her life has changed forever and she has to be with the baby. By being around you will be able to show that you are also being part of the change.
After a long session of nursing there is burping which can be taken care of by the dad while the mom stretches, grabs a snack or just a drink of water.
This is very important. If the mom eats right she will not get exhausted and tired and her health will also be maintained. Help her to have healthy snacks.
Small things like paying the bills, dealing with the grocery shopping, putting clothes away can be taken over as now mom is spending so much time breast feeding. She will feel happy and cherished and the house will look neat too.
If you have an older sibling then help to entertain, distract them. You can also help with their studies and the drop and pick up to school and classes.
This is very important. Mom needs a break. Pamper her and take her to her favorite restaurant or book her a spa treatment while you baby sit.
This ones a biggie. There is a constant battle between the generations on how certain things regarding child care and breast feeding are to be handled. The dad is the best buffer between the mom and well meaning elders in the house.
Always visit the baby's doctors with Mom. It helps if both of you would hear the instructions and it will help mom not panic and maintain clarity of thought if you can help ratify what the doctor said.