Today, we'll look at the traditional "stages" of grief. Dr. Elizabeth Kubler-Ross was the one to coin these, so I can't take credit. :)
The first traditional stage is Denial. Once the initial shock wears off, the character (or real life person) would pretend they hadn't just been given horrible news. A lot of times, they will just go back to work like nothing happened. This is really just avoidance behavior, trying to put off the inevitable.
The second stage is Anger. Whoever gets in the way here will likely be to blame. This can be explosive like a active volcano or simmering like lava. People will often question, "Why me?" and what they aren't saying is "Why not you?" They will be angry at anyone not affected by their tragedy, angry at God for allowing it to happen, angry at the deceased loved one for dying. Sky's the limit on how this might be manifested.
Third stage is Bargaining. This is when the character might seek ways out of their predicament, often in vain. They might bargain with God, hoping that if they agree to some action, God will reverse what happened. It's important not to write in someone in your manuscript offering the grieving person something they can't fulfill when the character is in this stage. Offering a person false hope during this time would be terrible.
Fourth is the Depression stage, perhaps the stage we most often associate with grief. This is when the character realizes what has happened is irreversible and they turn in to themselves. Anger and Bargaining are fairly animated phases, but depression is despair and hopelessness, an inactive phase of grief. Everything will be globally looked at from this lens.
The fifth stage is Acceptance. This is when the character comes to a place of being able to move forward with their lives despite the loss. This is when terminally ill patients begin making plans for their estate and doing things they have always wanted to do (think about the movie Bucket List).
I like to think about these phases as on a continuum. People don't always move through them one to the next (as the hurdles in the picture might suggest). Many cross between them or skip one or take two steps forward and one step back ("We go together because opposites attract..." Oh, wait. Got off track here!). Grief is so individualized, making it hard to pinpoint an exact process, so remember that while you're writing.
Good luck to you as you make your character's emotions as real as possible by incorporating some of these grief phases into your manuscript!