Write an article based on this "Pat it dry after washing. Fit it onto a head-shaped form. Allow the hat to air-dry."
Whether you washed it by hand or a machine, use a towel to blot out the excess moisture immediately afterward. Absorb as much water as you can. Reduce its water-weight to help preserve its shape as it air-dries. Be gentle as you do, though. Avoid crushing, denting, or otherwise marring the hat's shape. Ideally, use a mannequin head that's roughly the same size as your own. Otherwise, use a similarly sized round object (like a ball or rolled-up towel) to fit your hat onto. Set this on top of a dry towel to absorb any excess water that drips. Wool hats lose their shape very easily. For best results, wear it as it dries if possible. Never use a machine dryer. Expect the heat to shrink or otherwise warp the hat's shape. Let it dry on its own instead. Place fans around it to dry it faster if desired. A hair-dryer set to a low setting and held from a safe distance (a foot or more) is safe to use to make drying even quicker. Depending on the internal components, losing shape may not be as much of an issue for certain styles of hats. However, you still want to set it on something like a coffee can to keep the brim from resting on the wet towel.