Crying is not a weakness
The Prophet, peace be upon him, wept for his son Ibrahim. Quiet tears are permitted. What is rejected is loud wailing, striking one's cheeks and tearing one's clothes.
For the bereaved
Grieving is permitted
What is customary in the days after a death, what is permitted and what helps.
The three days
Taziya, offering condolences to the bereaved, customarily lasts three days. Grieving longer is not a sin, but after three days the community steps back and gives the family space.
Food comes to the house
In the first days the bereaved do not cook for themselves. Neighbours and the community bring food.
For widows
A widow's waiting period, the ʿidda, is four months and ten days. Special rules apply during this time. Exactly which ones differs between the schools of law. Your mosque will tell you what applies to you.
The prayer does not end
The supplication for the deceased continues to benefit them. So does ongoing charity in their name: a well, a book, something that benefits others.
Visiting the grave
Visiting the grave is permitted and encouraged, because it reminds us of our own end. Prayers are said for the deceased, not to them.
When children are involved
Do not explain death to children with metaphors
Children understand more than adults give them credit for, and cope with the truth better than with hints. Say that the person has died, not that they are asleep or have gone away. Anyone old enough to ask is old enough for an honest answer.
Whether a child goes to the burial is for the family to decide. There is no obligation either way.
You are welcome to call, even just to ask.
Not every conversation has to become a booking.