... It's not going to 'restore' your asphalt to the original look. The 'drippings' from you car actually attack the 'tar' in the driveway. The best you can do is 'pretty good job'.
Start by using a mixture of household dish detergent, like Dove or somethin'. Dump some water and start scrubbing with a bristle brush or broom. If you don't like the results, go to Home Depot or someplace, and ask for Asphalt Cleaner. It's a bit more caustic but may do a better job. Read the directions on the container BEFORE you leave the store in case you have any questions.
After cleaning, depending on how 'new' the driveway looks, it may be a good idea to reseal it. It's best to power-wash the driveway first, then seal. My best to ya and hope this helps.
PS: COnsider laying a 'black', old piece of carpet on the driveway to catch some of the oil. GO to a carpet store and ask for a remnant. THen, look into the cause of the dripping oil. It can be as simple as replacing a valve cover gasket or an oil pan gasket.