The time to consider this is when the purchase is made. Most things that say dry clean only, I put back on the rack. Many times manufacturers aren’t sure how to care for a garment and error on the side of safety. Sometimes dry cleaning is recommended because of buttons, dyeing techniques or trim. Start by reading the fabric content and directions. I would research the fiber online to start with, and read the directions on the garment. Most wool shouldn’t be washed, but some are made specifically for washing and generally are identified as “washable wool”. Many fine fabrics (rayons, some silks and many blends) can be successfully hand washed and reshaped to dry. A secret to success is using a small amount (more is not better) of mild soap or detergent and making sure to rinse well, really well. When you are done, do it again. Reshape and dry flat or hang to dry based on shape of garment.