I am not a grandmother but my oldest sister passed away a year before her grand baby twins were born. So I went up to help after the in-laws left. Since there were 2 there was a lot to do. And I did hold one as often as I could but while my niece was busy being a mommy I spent time cooking, cleaning up afterwards, went to the store if we needed something, took out the trash, and prepared bottles so all she had to do was heat the bottles up. Her sister and brother came - and couldn't find the dishwasher or wash a dish, nor could they fix anything. I even washed and folded clothes. So when it was time for me to leave my niece was ready to steal my keys. I didn't take over the house, I just quietly did things so my niece could relax. Since there were 2 she pumped instead of feeding straight from the breast so she needed the quiet time while the babies slept to relax and that was when I did a lot of the work.
My MIL did nothing when she came after my DDs were born. So instead of taking care of a baby I had to cook, clean and watch after the in-laws. (I could hardly wait for them to leave.) My parents came and when my mom made dinner she made enough so there would be left-overs. And when she made soup she made enough to freeze so it was there after they left. My dad was never one to cook and clean but he was great at holding the baby so I could cook or do laundry - whatever I wanted to get done.
Just be helpful. And enjoy the new baby - wish I had one, I really loved helping with the twins.