Assuming it is a first time mother:
Main job is as gatekeeper - allow you the visitors you want, keep away those you don't, throw out those who have overstayed, make tea for all of them. Ditto screening phone calls - he can take most of them and only pass across those you want to talk to.
Provide new mother with constant supply of water, tea and coffee (don't wait to be asked), ensure she eats, take baby while she does eat (as babies somehow know to scream everytime food hits the table), keep fridge stocked up with necessary foods.
Tell her that everything she is doing is fantastic, you are very proud of her, you think she and baby are wonderful and you love them - self confidence is very low in new mothers and they need as much boosting as possible.
Make sure that when the baby is settled new mother gets as much sleep as possible - during day as well as night - and not rushing around doing pointless "essential" tasks like cleaning the worktops in the kitchen. Put her to bed if necessary.
Write as many thank you letters for presents and flowers as possible so she doesn't have to do it.
Do as much with the baby as you can, (nappy changing, winding, taking it for walks, baths etc) but don't take it personally if she appears to criticise the way you do it all - ride with it and tell yourself it will get better soon.
Don't take it personally if you find her in tears for no reason at all - hormones - just keep telling her how wonderful she is.
If your mother arrives to help, keep a close eye on how it is going - if she appears to be winding your wife up, whether or not you think it is justified - try to step in and defuse the situation
That's all I can think of for now!