You obviously cannot leave your shawl to the machine. The fabric will simply pull out. The best method to wash is to hand wash, separate from all other clothes. Fill out a tub with cold water. Mix in a good quality detergent like Woolite. Put in the shawl and slowly roll it inside the water to wet all sides. Let it soak for around two minutes and not more than that. Take out the shawl and place it in the sink. Now empty the soapy tub, rinse it and fill with clean water. Put in the shawl again and swish it around to get rid of the soap in it. Repeat the process to get all the soap out of the shawl.
Now bloat out the excess water suing towels. Do not wring the shawl at any cost. Lay it on a drying rack to air dry slowly.
If you want to press the shawl, place a fabric between it and the iron and do so on low heat.
Storing a Pashmina shawl:
You will not be needing the shawl in summers. If you want to store your shawl for the season, spread it out on a flat surface. Now cover the top with tissue papers laid out. Once all of the top is covered, fold the shawl in half. Cover the top again with tissue and fold again. Keep doing it until you have folded it to a size you want. The tissues help in keeping out wrinkles. Choose a storage place that is dry and out of sunlight. It should be cool. Take out the shawl in the next season when you feel like going out in class.
Care is needed not just during washing, you have to do it all times, including those when you wearing the shawl. Keep it way from any pointed object that can tear it. Also try your best to not spill anything on it so that your do not have to wash it frequently.