If the oil spot is recent and is wet, then gather a clay-based cat litter, sand, baking soda or cornstarch in order to absorb the oil. This method leaves nothing but clean concrete behind. If the oil spot is not recent and has dried, then the area needs to first be wet with water. Afterward, use a stiff brush with a water and baking soda mixed paste. Let this sit for a few minutes and then take a hose and wash the area. Finally, let the concrete air dry.
For harder oil spills, try using a household or chemical cleaner, such as a concentrated laundry detergent. Pour this on to the area and let it soak for a few minutes. Then try scrubbing rigorously and hosing the area; this process may need to be repeated several times if the stain doesn't come off. If these methods do not work, then a professional concrete company may need to be called.