Vacuum thoroughly, and use a soft brush (ie. new toothbrush) to raise the loose dirt to the nozzle. Soil sometimes can be softened and removed using baby wipes. For oil stains, use some brake cleaner (hydrocarbon based is better than "green") sprayed on a clean wite rag (flannel or towel) to carefully daub at it. The white rag won't transfer colour, and you can see if it's lifting the stain, and monitor your progress.
In all stages, gently, gently!