Cradle cap usually resolves itself within a few weeks or months. But you can speed up the process using home remedies that is already available in your pantry.
Use a gentle brush to and comb it back wards to remove the dead skin from the scalp. Oiling the scalp would have moistened the dead cells making it easy to come off of the skin.
Wash with a mild baby shampoo. You can do this twice or thrice a week. Also, contrary to popular belief, washing too often is not beneficial to your baby.