Shiva is the seven days immediately following a Jewish burial. It is the very beginning of the mourning process, a process that can take a lifetime. Typically, the mourners stay at home, and members of the community come to call. Not so much to console, but more to show support and sympathy. There are many customs surrounding this ritual, they differ from community to community. Some things hold true no matter what the prevailing custom may be, what religion you do or do not practice, or what your beliefs may or may not be. Here is an interesting take on how and how not to behave when making a shiva call.
While this specifically addresses issues surrounding the actual shiva period, many of the thoughts and recommendations apply far beyond those first agonizing days.
I mentioned that often the best thing one can say to a mourner is nothing. This article explores why that is true. Here is a suggested way to approach someone who has lost a loved one that works for many weeks, months and years afterwards. There is no expiration date on empathy. Compassion and consideration don’t have a shelf life. Sometimes just being there is enough.