You can get a oil leak on your concrete drive at any time from your vehicle. Or even a oil stain from a fish fryer, what ever reason it will be leaving a stain. It doesn't have to be just your driveway it could be your garage floor as well. If you don't clean up the stain, be prepared for it to be there for ever. It can also become a safety hazard or dust gatherer as well.
You will want to apply some absorbent material to your oil spill. This will prevent it from getting worse, before you can really clean it up. As soon as the spill happens the best thing to do is get a roll of paper towels or a old rag and try to absorb the stain. Another option would be to use sawdust or cat litter, and let it sit for 24 hours before cleaning it up. For warm oil you can use paper towels and rags as well. Squirting liquid dish washing soap and some water on it will help also. The soap will surround the oil spill and keep it from solidifying. Of course you can also purchase oil cleanup compound at any automotive store.