Rub mild soap gently into the creases. Clean the dirt out of the creases with the soap and water.
Stuff the shoes with paper or rolled-up fabric until they are stretched out to their full shape. Place a damp cloth over the creased areas and iron the shoe through the cloth.
Spray the stuffed shoes with water until the fabric is fairly wet. Place a few books on top where the creases have formed. Leave the shoes to dry.
Take out the stuffing and spray the shoes with water. Put the shoes into the dryer and tumble dry on a low setting. Check on the shoes every 10 minutes since you do not want to expose them to any more heat than necessary.
Use a soft rag to rub shoe polish that matches the color of your shoes into any remaining creases.