My friend noted that he heard two things at almost every wake. 1) What can I do to help? and 2) some variant of "If there is ever anything they need let me know" He noted how he thought this odd that the visitors would speak to him about this, as he was unlikely to be very involved in people's lives after the funeral. He decided he would keep a calendar book handy at wakes. When people indicated they didn't know what to do but that they were willing he would take out the book and say, "there is something you can do. How about setting a date and time with me when you will go visit the bereaved family " That was it. It was simple and powerful because all it required was a visit and no special skill or obligation.
Later in my own conceptualization I used the mantra" Be there and listen". People need people and company and they often need to talk and relive their loss and the emotions that come from it. It is incredible how effective it can be to simply allow a person to talk it out.