Black cars are brutal
Two bucket method as stated above.
If you need to clay the car, any of them work fine. You can pick these up at any Autozone
Wash in a straight line how the wind would flow over the car will help prevent some swirls. Wash from the roof down. Then again, as stated above, sheet the water off the car with the end of the hose, not using the spray attachment. By doing this most of the water will come off the car leaving much less to "dry"
I lay the waffle weave on the wet spots on the car and let the towel absorb it, then I remove I rarely if ever "wipe"
To dry I use a waffle weave microfiber towel
Can get them here along with you microfiber polishing towels:
Microfiber/Waffle Weave Drying Towels
For polishes I use Poorboys. Love them because, not only do they do a great job, you can use them in the sun:
poorboysworld.com
To apply polishes I use a porter cable. Nice kits sold here:
Dual Action Orbital Polishers and pads: Porter Cable 7424 : Lake Country Buffing Foam Pads
I also love Poorboys trim restorer for the front air dams and actually the tires and weatherstripping too. Makes them black but not a wet shiny black like with some tire foams and treatments:
poorboysworld.com
Another product I love to use after I polish is a glaze. Glazes typically help fill in swirls you can't remove and deepen the paint.
RMG is my all time fav. Makes the paint look warm and buttery AWESOME!
ClearKote Red Moose Machine Glaze
Finally is one of my most versatile and useful products and that is the quick detailer!
This is one of the most important products as it limits the times I need to wash the car.
The best IMO is Finish Kare's FK425
Finish Kare FK1 Consumer Detailing Products You'll have to scroll down
Also, I'm not sure why you wouldn't wax the car. Just helps to maintain that nice finish longer and to help prevent frequent polishings (which technically removes clearcoat)
I love how a carnuba wax looks on a black car. Finish Kare has a nice one that is really resiliant in their Pink Wax (same link as above)
But when I'm going for that super warm jaw dropping wetness in my paint I use S100 (similar if not the same as P21S). Doesn't seem to last as long as pink wax, but it looks better IMO:
S100 Carnauba Wax is a hand-poured blend of German waxes, proprietary ingredients and pure Brazilian Carnauba wax. motorcycle wax, bike wax, s100
This can be found locally at any Harley shop too (usually)
I usually apply this with the porter cable and a grey/black finishing pad then wipe off with the usual microfiber.
Hope this all helps. Keep in mind these are just my fav. products. Others may have different opinions