Use a spoon to remove the pumpkin skin from the cooked pumpkin. You may be able to lift it off in one piece. If not, just use the spoon to tear off the skin in pieces. Now you are ready to puree the pumpkin.
You can use an immersion blender, a food processor, or a blender to puree your pumpkin. Just use which ever one you already own. I pureed one half of the cooked pumpkin at a time using my immersion blender.