Probably the most famous formulation of the stages of grief was developed by Dr. Elizabeth Kubler-Ross in her book "On Death and Dying". Dr. Kubler-Ross actually wrote about the stages that dying people tend to go through as they come to terms with the realization that they will soon be dead. However, her stages have since been borrowed by the larger grief community as a means of describing the grief process more generally. Coming to terms with dying is certainly a loss experience and an occasion for grief, so there is merit to this borrowing and reason to become familiar with Dr. Kubler-Ross' stages. Again, not everyone will experience all of these stages, or, if all are experienced, they won't necessarily occur in this particular order.
Kubler-Ross' first stage is Denial. In this stage, grieving people are unable or unwilling to accept that the loss has taken (or will shortly take) place. It can feel as though they are experiencing a bad dream, that the loss is unreal, and they are waiting to "wake up" as though from a dream, expecting that things will be normal.
After people have passed through denial and accepted that the loss has occurred (or will shortly occur), they may begin to feel Anger at the loss and the unfairness of it. They may become angry at the person who has been lost (or is dying). Feelings of abandonment may also occur.
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Next comes Bargaining. In this stage, people beg their "higher power" to undo the loss, saying things along the lines of, "I'll change if you bring her (or him) back to me". This phase usually involves promises of better behavior or significant life change which will be made in exchange for the reversal of the loss.
Once it becomes clear that Anger and Bargaining are not going to reverse the loss, people may then sink into a Depression stage where they confront the inevitability and reality of the loss and their own helplessness to change it. During this period, grieving people may may cry, experience sleep or eating habit changes, or withdraw from other relationships and activities while they process the loss they have sustained. People may also blame themselves for having caused or in some way contributed to their loss, whether or not this is justified.
Finally (if all goes according to Dr. Kubler-Ross's plan), people enter a stage of Acceptance where they have processed their initial grief emotions, are able to accept that the loss has occurred and cannot be undone, and are once again able to plan for their futures and re-engage in daily life.