For stubborn stains, try rubbing the spot with a white eraser, but be gentle and check whether it aggravates the problem before rubbing the entire area. Soak up oil spills with cornstarch. Apply the dust to the area and let it sit overnight. Dust it off the next day.
Deal with stains as quickly as possible so they do not have time to harden or stain the leather. If necessary, seek professional assistance.