Ensure that your ironing board and iron plate are pristinely clean and dry before ironing.
Set the iron to silk temperature (around 148°C / 300°F).
Place your scarf dull side up if - or if it has no dull side, place either side up and use a pressing cloth. Press your scarf, avoiding the hand-rolled edges so as to not permanently flatten them.
DO NOT use the steam setting as this can create water stains on your silk. If you like the look of folds marks in your scarf, you can fold your scarf and place a pressing cloth over it and iron the folds in.