ughhhhh....... I should be ashamed of myself.... I haven't washed ANY of my scarves since I bought them LOL! but if I were you I'd just take it to the drycleaners, or if it's not THAT dirty, just soak it with warm water.
I wouldn't even risk it soaking in the water! The dye might come out of it or something, especially if it's a dark colored shawl. Take it to the dry cleaners, and then leave it in the cover that they give you until your next wear.