Starting in Genesis we can read about how people mourn. In Genesis 37:34 Jacob tears his clothes, puts on sackcloth and publicly grieved. Jacob wasn't the only one to mourn like this, Job did it after his family and possessions were taken from him and Jonah did as well. Those are still only a few of the examples in the Bible of mourning and wearing sackcloth.
It was common for them to tear off their clothes and then followed up by sometimes putting on sackcloth. Sackcloth wasn't a warm and fuzzy outfit, it's more like a rough, course, and ugly garment. These are some ways that you could show your grief publicly.
There were other ways to show grief as well. Singing songs of lament, coving yourself in ashes, hiring mourners to stand around you and cry, removing shoes, public crying/wailing, fasting, shaving your head, not saving your face, wearing dark colors, and so many other ways. Mourning was a public thing, it was something done in a community. When one person would mourn, others would recognize and come to comfort their friends and family as part of a community.
Some of the ways we mourn today still follow some of the biblical models. In America it's common for someone who has lost a love one to wear black and to surround themselves with family and friends. In Jewish families, the loss of a loved one causes a period of mourning that is even closer to the biblical model. I could try to explain it, but I am sure I would mess some of them up, but they have guidelines about what clothes they can wear, about tearing their clothes, about showering, their diet during that period and even looking in the mirrors. Mourning is important. It's a way for us to expel our emotions and move on from them.
Grief and mourning are more than just for the death of a family member or friend. I think this is where we sometimes forget that mourning is for more than just for dealing with death. And mourning is not something we are supposed to do alone either. God made us to be social creatures. He gave Adam a partner because He knew that we needed other people. If we were meant to sit alone in our pain, then God wouldn't have blessed marriage and families and created friendships.
So when we are mourning, we should allow others in. We can't shut them out. God created others so we would not be alone. Who are we to say that we can do it alone?
We also need to pay attention to those around us who are hurting. We need to support everyone who is in pain, whether they are friends and family or strangers to us. It's our job to love others in our community and be there to support them, physically, mentally, and spiritually.