Etiquette and nichum aveilim
Things not to do:
Don't try to comfort the person by saying "it was their time to go." Rabbi Yaffe said that some people say that even to parents who have lost children. It's not appropriate to make any such statement, nor to point out to parents that they still have surviving children.
Don't start criticizing the avel in any way, shape, or form. That extends to the situation of the niftar or even the setup for the shiva house. My husband's mother has a dog that she kept upstairs most of the time when people were dropping in. One visitor said she was being cruel to the dog, which hurt her feelings quite a bit.
Things to do:
Say it with food seems to be the motto of the members of the tribe. During shiva a lot of food is sent over by well wishers. Much of it is used and very much appreciated. But some really goes to waste. During the shiva, my husband's family threw out whole huge fruit platters that remained untouched after a few days. They happen to not be big on fruit and hardly made a dent in all the fruit sent. Yes, fruit platters are nice, but they don't keep fresh very long. So it's a good thing to check ahead about the family's food preferences and what they have. When in doubt, send something that keeps longer. Another nice thing to do is to find out about what foods they really shouldn't have, like deli meats that are high in salt for people with high blood pressure.
Do call if you can't come. The Kveller article said coming in person is what it's really about. That is true, but sometimes it really is not feasible. I can tell you that my husband who is really not a phone person still appreciated getting calls from people he feels connected with when they couldn't come in person, particularly as he was sitting away from his own home and was most often surrounded by people he didn't know.