You could say,
“I’m going to the market this afternoon. What can I bring you from there?” or
“I’ve made beef stew for dinner. When can I come by and bring you some?”
If you’re able, try to be consistent in your offers of assistance. The grieving person will know that you’ll be there for as long as it takes and can look forward to your attentiveness without having to make the additional effort of asking again and again.
Shop for groceries or run errands.
Drop off a casserole or other type of food.
Help with funeral arrangements.
Stay in your loved one’s home to take phone calls and receive guests
Help with insurance forms or bills.
Take care of housework, such as cleaning or laundry.
Watch their children or pick them up from school.
Drive your loved one wherever they need to go.
Look after your loved one’s pets.
Go with them to a support group meeting.
Accompany them on a walk.
Take them to lunch or a movie.
Share an enjoyable activity (sport, game, puzzle, art project).