Well I'm white, but it should still apply to all races.
You gotta shave right after a shower. No way around it. Make sure to wash your face in the shower also. Helps clean everything off your face. The warmth from the shower opens pores. Don't use cheap shaving creams or gels. What I use, and love is C.O. Bigelow Premium Shave Cream. This stuff goes a loooong way.
Next up is....Get a shaving brush. Really. This also helps with getting the hair on your face ready to be shaved. You can find one for a reasonable price. Just make sure it's Badger hair.
Next is....Let it grow out a day or two to see how the hair grows. Different places on your face has different directions it grows. Always go with the grain initially. Very Important. Don't go over the same spot multiple times. If you have to use short strokes and rinse a lot, so be it. These are the two main reason you get razor bumps.
Don't fall into the hype of a razor with 4 blades, 10 blades. Use what works best with your face. Some people use cheap disposable razors with a single blade, while others have the same results with the 3-4 blade razors. Just make sure your razor is new to fairly new. Sharp blades = happy face.
So right after the shower, you hop out. Get a face towel, and everything else you need to shave. Make sure you splash some more warm water on your face. Wet your brush with warm water as well. Put a bit of cream on the brush and work it into and all over the places you want to shave. Remember, with the grain initially. Short strokes if you got a lot of growth you're shaving. At the end, feel with your hands to see what might need to be gone over a second time. Gently go in a cross/side motion from how you just shaved to get it baby soft.
When all done. Splash cool water on your face. This closes the pores back up, stops or slows any bleeding. Pat face dry. Now you must moisturize. White, Black, Asian, it doesn't matter. Gotta keep your skin healthy, and looking good. Helps with future shaving. Best bet is to go with something with No Alcohol, or Fragrance. Those will irritate your skin like no other. Something with good vitamins for your skin. Get something that also has a SPF of atleast 15-30 in it. I alternate between stuff with, and without SPF in it, just so it doesn't clog up the pores.
Here is a place with these steps I just listed.