Everyday dirt can be removed with a small brush, either a natural gum latex or a fine wire brush. Another approach is to use simple hand soap and water on a facecloth or sponge and wash the upper leather. After washing it is best to allow the shoes to dry in the air. It is never recommended to use heat to dry leather as it tends to stiffen the leather.
Oil stains on nubuck and suede are stubborn and are difficult to remove. If you happen to get a stain on your shoes (especially oil or grease), try to blot with whatever absorbent material is handy. Sooner is better as the stain may sink in. DO NOT use water as it may cause the stain to set. Sprinkle the stain with baby powder or any kind of talcum or chalk. DO NOT rub it in, but simply let it sit on the surface. Let it sit overnight and then lightly brush it off in the morning. Then you can use a nubuck/suede brush, or any stiff brush such as a nail brush.
If there is still a stain, you can try using a commercial degreaser. If this leaves the stained area lighter, you might consider applying the baby powder and degreaser across the entire shoe.
Another technique is to use an abrasive cleaning eraser, just as you would use a gum eraser on paper. It is a good idea to finish the cleaning with the nubuck/suede stiff brush.