Hang the drapes as planned. Mist with a wrinkle release spray. Gently pull and smooth the fabric to remove the creases. Wrinkle release sprays can be purchased where laundry products are sold or you can make your own by mixing 1 cup of water with 1 teaspoon of liquid fabric softener in a spray bottle.
Fill a garment steamer with water and adjust the heat setting to the appropriate level for the drapery fabric. With the drapes hanging, hold the steamer upright and aim toward the creases. Occasionally pull the garment steamer away and smooth the fabric with your hands. When all creases are gone, allow the drapes to dry naturally.
Machine wash drapes in a warm, short cycle to release the creases. Place in a clothes dryer at the highest temperature the fabric can safely tolerate for five minutes. Reduce the temperature to a cooler yet still warm setting for up to 10 minutes. Complete the process with 10 minutes of cool temperatures to keep new creases from developing. Remove and hang promptly.