The goal of the mourning is NOT to comfort the mourner but to allow them to get fully into the grief and fully experience the loss. It is only when people have full grieved that comfort is possible. So, to allow this to happen, Jewish tradition tells us the following:

a. Don't try to change the topic from mourning to lighter and more pleasant topics. The most appropriate topic of conversation is about the deceased and her/his life.

b. Allow the person in mourning to set the conversation. Don't initiate the conversation, but allow there to be long periods of silence until the prson in mourning decides to initiate a conversation. It's ok to be with someone in silence.

c. Don't call the house of mourning on the telephone. Just come to visit.

d. Don't bring or send flowers, as though the goal is to cheer things up. DO bring food for potluck and also for helping the mourner not have to cook in subsequent days, fruit, and other things that will make it
possible for the person in mourning to not have to focus on survival needs (doing chores, laundry, other things of that sort are appropriate offerings). The point is to free the mourner from all tasks so that s/he
can be fully into the mourning. Similarly, the best way to help is to jump in and help, not to ask the mourner to give you directions in helping. In the best circumstances, a close friend becomes the aide to the mourner, directing other people and giving guidance so that the rest of us can figure out what kind of assistance is most useful.

e. Avoid seeking reassurances that you are really helping. One of the biggest distractions in the mourning process is that friends and others who love the person in mourning often create the feeling in the mourner that they need to be reassured that they are doing the right thing--and this then creates a dynamic in which the mourner has to take care of those who supposedly came to take care of the mourner.

f. There are no appropriate kinds of clothes to wear. The notion of "black" for mourning does not come from our tradition. The people in mourning themselves are supposed to wear the clothes that they were wearing at the time they learned of the death and tore their garment in symbol of the loss. They are not supposed to focus on their appearance, clothes, or anything else besides mourning (which is why it is traditional to stay at home for seven day and not go to work or other distractions from the mourning process).

g. There is no shiva and no mourning on Shabbat. The mourner traditionally comes to Friday night services, but does not enter the service until after the joyful part of Lecha Dodi is concluded (in our
community, it would be appropriate to wait till after the dancing for tov le'hodot). The mourner says kaddish. Though others may feel the loss, the tradition is to let the people who are actual relatives say the kaddish by themselves.

h. The mourner traditionally sits on the floor or on a low bench, and those who come visiting should try to do the same.

i.. The traditional way to end the visit to a house of mourning is to say: "Ha makom yenachem etcham toch sha'ar evley Tziyon VeYerushalayeem" (May God comfort you along with all the mourners of Zion and Jerusalem.).
Again, this way of leaving is meant to replace the tendency to try to say some vacuous "uplifting" statement that misses the point that THERE REALLY IS SOMETHNG TO MOURN and no, it's not going to be all right, because someone very valuable has been lost to the world.