One of the foundations of Judaism is the idea of emulating the ways of G-d. Comforting mourners, Menachem Avelim, is one of the acts of kindness (chesed) that give us this opportunity. Ideally, you should visit a mourner during the shiva (the seven-day mourning period that commences after the funeral). Although our basic requirement is to make the mourner feel better, the idea is not that we should try to take his/her mind completely away from their pain. A mourner has to come to grips with his/her loss, learn to accept it and not ignore it. The conversations should be limited to memories, hope, consolation and comfort. Showing your empathy and caring by listening or even just entering and not speaking gives comfort and honors the mourners. You are not allowed to greet a mourner or say goodbye, rather you should wait until the mourner begins speaking before saying anything. Upon leaving the mourner, the traditional "HaMakom..." phrase is recited which can be found in any siddur (prayer book).