The best way to offer sympathy depends on how well you know the grieving and deceased persons, but listening, being present, and avoiding clichés or negative statements are very important. Saying, "I'm so sorry that Mary has passed away," may be all that is needed.
Grieving people often take great comfort in hearing positive stories about the deceased. If a person is uncertain of what to say, they can tell a story or mention a positive trait about the decedent, such as "Mary was such a caring and helpful person, and she will greatly be missed by all of us." Other simple statements include "you are in my thoughts and prayers" or even, "what I am feeling now is hard to express with words."
When offering sympathy, the ending is important. Expressing ongoing love and support can be helpful to the grieving person. An offer of calling or visiting next week may alleviate the loneliness that the grieving person will most likely feel, when the funeral is over and others have returned to their daily lives. In order to demonstrate the sincerity of the statement, it is important to mention a specific day. When offering to call or visit, it is also important to follow through.