What to do when someone passes away...

My mother passed away a week back. She was 61 and had a cardiac problem for the last 7 years. She was a fighter and lived on willpower.
A lot of people came to meet us. Some said some things, others just didn't say much. I got several mails, several messages. In general people were very kind.
A lot of people I know, especially those my age or younger said they didn't know what to do or say.
I agree, it is very difficult to know what to do/say to the bereaved family in such times. Nobody tells us what we should do. There is no specific training given to us.
So now, having been on this side, I can tell you what helped me. The following is simply what I experienced in an Indian setting where the funeral happens the same day as the death. It may be different in other countries where the funeral takes place after a week or so.
1) What helped us was that we were the first priority for most people and they took care of us really well.
2) What should you say? I think you should say as little as possible. During the funeral/vigil, the bereaved family is not able to grasp much of what's happening around. The deceased is technically gone but is still there in front of them. For the family, this is actually the last time they look into the face of their loved one. They may be saying things to that person in their minds. It's best to leave them to it.
3) It helped me when I cried. We had known for more than 12 hours that it was all over. All the stress, all the worry, all the sadness needed to come out. So it was a relief when my aunt asked people not to stop me from crying and said, 'Let it all out beta'.
4) People were concerned that I may cry too much and faint or something. The glasses of water kept coming and that helped a lot.
5) I was infinitely grateful to see a few people who didn't even know my mother and who simply came to help out. My husband's friends, my bil's friends...With them around, I felt that I could now leave the organisation part and simply spend the last few moments looking at my mother.
6)The funeral is not the only time one needs support. Grief comes in spurts that continue for about a year. If you are present at a spurt, just talk to the person as if he/she is not crying. Don't fret over the crying. It will subside. Atleast some pain is being let out.
7) We do not follow the customary grieving period and are relieved when people simply take us back into social life. It'll hurt if people expect us to remain absent at events because 'they' believe in the grieving period funda. So don't worry about taking a grieving friend out for a movie or a walk. They probably want it too.
8) Grieving friends will tell you how tedious it was to repeat what happened to everyone. They're right. Generally when we tell someone how the person passed away, it takes us back to that day and gets painful.
9) We had a remembrance meeting to celebrate mom's life. It was a way of talking about her life of 61 years rather than her death. That helped a lot as it brought her back to life in the form of positive memories that people shared.
10) All in all, we are strong thanks to all the people who keep coming over, calling us, texting us, sending us mails, messages etc. We cannot describe in words how thankful we are to have such a wonderful loving extended family who took over and ran our house for 4 days and who helped us deal with the loss. Our friends who make sure to drop by and see how we are doing from time to time. You are never going to imagine how important you all are in these testing times! Thank you!