Soft, lightweight sheers tend to build up static and may stick to the iron as you press. Work slowly so as not to accidentally press creases into the fabric. Use a Teflon shoe on your iron if you have one. If you do not cover the sole of your iron, check to make sure that there are no nicks or scratches on the sole to catch the fabric. Fabric-covered seam rolls and hams can be used to press seams and darts but avoid wooden seam sticks unless they are covered with fabric as your silk fabric may catch on the grain of the wood if left uncovered.
Use a medium setting on the iron and do not use too much steam, which can change the texture and may blow wrinkles into the fabric.