Condolence money is typically given as a gesture of sympathy to people who are suffering from sadness due to a divorce, rejection, a person's death, or some type of loss. Giving a gift demonstrates the giver's support of the receiver in this time of sorrow. The type of sympathy gift depends on the culture of the deceased person. Sympathy flowers are also a form of a condolence gift, but there are times that the families ask that condolence money be given in lieu of them.
Although people may assume that sending money is appropriate in all situations, this is not the case. It is true that many people may actually be offended by receiving such a gift. Someone who is mourning may think that by receiving money, it is suggested that material things could ease the person's pain. An example of this is when the operator of Tokyo Electric Power Co., Japan's nuclear power plant offered money to the victims of the nuclear crisis. Even more money was offered to those who suffered from a death. He did this voluntarily and was not in any way obligated to do so. Out of the ten towns in Japan the so-called "apology money" was offered to, one town did not accept it because they did not believe that money would make up for the tragedy. Their good health and lives as a whole were compromised due to the radiation exposure, and money was simply not going to amend that. The amount of money given was not even large enough to cover all of the financial losses from the crisis. Those who did accept it, however, despite the tragedy, chose not to speak badly of TEPCO.
This large-scale situation is an example of when sending condolence money might be inappropriate, despite some groups of people's willingness to accept it. In the scenario of one person's funeral, however, it is best to use your discretion on whether to give money or not depending on the family's financial difficulty or perhaps upon their request. It can assist them in paying for any expenses relating to the loss, such as the funeral, casket, or burial plot.
In terms of how to physically present the money, in the Japanese culture, they give the receptionist the money in a unique envelope with black and white ribbon tied around it and the amount of money written in front. It is given to the family after the service. For the Protestant and Catholic religions, people directly donate the money to the church or charity of the deceased person's affiliation.
The amount itself is contingent upon one's relationship with the person who has passed away. It is likely that if you were very close to the person, their family may expect a larger amount than from those who were simply acquaintances to him or her.