When one pays a shiva call, the focus is on comforting the mourners in their time of greatest grief. Traditionally, one enters the shiva house quietly with a small knock so as not to startle those inside. No one needs to greet visitors; they simply enter on their own.
Food or drinks are not laid out for the visitors, because the mourners are not hosts. They do not greet the visitors, rise for them, or see them out.
When entering the house, you should not greet the mourners. In fact, it is best to come in silently and sit down close to them. Take your cue from the mourners. If they feel like speaking, let them indicate it by speaking first. Let them lead and talk about what they want to talk about. It is best to speak about the one who has passed away, and if you have any stories or memories to share with the mourner, this is the time to do so.