Forgive me if I am wrong, but most of the answers to the "what I do now" sound cold and just addressing the "practical" and task oriented phases of dealing with a loved one's death.
It seems to me that the question is more on the emotional side. "My father just died, what do I do now?" can be easily interpreted as "Oh, my God, I just lost my father who was a huge part of my life, my rock, my best friend. I am so much in pain that I do not know how to go on with my life."
The answers that somewhat addressed this issue directed the person to links for grief support. That's great. However, aren't these people sharing their grief here and looking for comfort? If so, why not share with them how we coped with losing a loved one, like a parent? Sharing our experience might help them cope with theirs.
I lost my mother to breast cancer over twenty years ago. Although I knew that she would eventually die of the disease (stage IV), it was not any easy on me to know this fact when she died. After she died, I felt I was in limbo. I went through the "practical" tasks described above as in a daze. I was her only child and everything fell upon my shoulders. Everyone else in the family seemed to disappear as if by magic, leaving me alone with my grief. Fortunately, my son was only three years old and as a single parent, I had to "hold it together" for him. Having that responsibility certainly helped.
Nevertheless, the "being in limbo" feeling took months to go away. Also, to my surprise, I seemed to have "adopted" some of my mother's personality traits for a while. Going through her stuff was a painful experience. I think it is best to leave that "task" alone for a while instead of diving into it right away while the grief is still in "raw form".
As time went by, I allowed myself to cry my eyes off when alone. It brought some relief. I also found that what worked for me for a while was to avoid anything that had to do with my mother, even thinking about her. I think that is one of the stages of grief. As getting angry towards the departed is another stage. I did. I was very angry at her for a while (especially since she had refused treatment after her mastectomy). I felt betrayed. I felt abandoned. Of course, then, I felt guilty for having those feelings.
Allow yourself to grief fully. Don't let other people rush you through the grieving process. There is no set timeline. Some people, like me, take longer to move on. Others are able to overcome the grief and move on with their lives almost immediately. Each one of us have our own way of coping. Find yours. Perhaps, writing how you feel might work for you. Or, acting as if your father were still around and having imaginary conversations with him. You will say good-bye to him in your heart and mind when you are ready. Cherish the memories of the moments you had together. They will always be with you and your father remains in your life through those memories. Allow yourself to feel his presence. The body is the only thing that dies. The body is just the vessel that our spirit uses to function in this physical world. The essence of our being is eternal. Your father is still alive either in another realm or here in spirit form looking over you until you are able to overcome the grief and move on, There's no rush. Just allow yourself to take it one-day-at-a-time until you're ready to let go. It might take you days, weeks, months, or even years. That's OK. It's your life, not anyone else's.
Hope this helps. :)