Start by sweeping your blacktop surface free of accumulated dust, leaves and other debris. Use a wide push broom with stiff bristles, or clear all the nooks and crannies with a Shop-Vac.
Clean the blacktop with a solution of laundry detergent and water. Use a bucket big enough to dip your push broom or a long-handled coarse scrub brush into. Pay special attention to any tiny cracks where dirt may be lodged or moss may be taking hold. Rinse thoroughly with a hose.
Attack grease stains with a solution of trisodium phosphate (TSP) and water, or use Spic 'n Span or another phosphate-free cleaner if you're concerned about the runoff. Let the solution sit, then scrub with a brush and rinse thoroughly.
Try a little undiluted household chlorine bleach on stubborn stains and marks. Be sure to wear gloves and eye protection, and rinse thoroughly.
Turn to a specially formulated blacktop cleaner like Latex-ite if household remedies don't suffice. You can connect the Latex-ite bottle to a garden hose or power washer for ease of application, and then flip a switch on the bottle to get a plain water rinse.
Finish with an application of a blacktop sealer if your driveway or tennis court is free from cracks, and it's been at least three years since it was last sealed. Repair cracks and fill holes before sealing, if necessary. (See the related eHow article, "How to Patch a Blacktop Driveway.") You can get water-based sealers that are environmentally friendly, though traditional coal-tar sealers stand up better to oil and grease stains.