@Sausages999 The first thing I would say (my mother who I was very close to died) is that you cannot, absolutely cannot properly understand what it is like to have a parent you love die until it happens to you. You think you know how awful it will be and say all the right things - I certainly did - but when it happens you realised you had no idea. So I think you need to understand this first and foremost when dealing with your father. You just will not properly understand the depth of his grief.
Second thing is that if his father has died previously, he will have had this experience of the hell that is parental bereavement already. He will know how it goes and what to expect so although all grief is different, he is already better prepared than when his father died.
I would be lead by him. Everyone grieves differently. Offer him opportunities to talk about his mother if he wants to. If he doesnt, don't push it. He may just want a hug. He may want to be left alone. Everyone copes differently.
If your father lives alone, practical stuff like turning up to cook him a hot meal may be welcome.
It is helpful to be with people in the same situation so if he has siblings, very much encourage and enable him to spend time with them if he gets on with them and its practical.
It is definitely worth considering grief counselling. Cruse and other organisations offer a free service but there can be a many month waiting list. I was told that you should wait to start counselling anyway because in the first few months it is all still raw. I didnt really understand why or how it would be helpful but it made such a difference to me and Id strongly recommend it.
another thing - maybe not right now - but in a while when its less raw is to think of ways you/he could honour and memoralise you grandmothers memory - plant a tree in your garden on the anniversary of her death, sponsor a bench with a plaque to her memory in the local park or library or where ever she liked to go.
Ultimately, when the chips are down though, there is really very little anyone can do that makes a difference because it is only time and more time that can do anything really.
Overall just stay in touch with him regularly and let him know you love him. Texts, calls, visits mean the world from those you love.
I'm sorry for your loss too - because you have lost a grandma - its not just about your father. Look after yourself too.