it really depends on two things in my book.
1- what does the person look like?
in order for others to perceive you as black, you must have a dark skin tone, however slightly dark. or you must have features that appear african in descent (vin deisel anyone?) your phenotype, or the way you look on the outside will effect the way folks respond to you. you could have lots of white blood or otherwise, but if you look black, you are treated as black. that's something tiger woods has yet to figure out but it's a fact nonetheless.
2- how does the person identify?
if you look almost white and you don't claim being black then you are perceived as white (vin deisel anyone?). if you look brown or near so in complexion, have some black ancestry and you claim to be black, then you will be accepted as such.
frankly there are lots of white folks walking around with black blood, but they don't look it and they don't own it. so they're white. there are lots of black folks with white blood, but they don't look it (or may look it) and don't claim it. so they're black.
the concept of race was made up by early colonists. it stand for nothing but the color of your skin. and it's rediculously exaggerated. let's face it, no one is really white except albinos and most blacks in actuality are closer to brown than black. it was made up as a divisive technique. and it worked didn't it?
i think it may be safer to refer to the term "people of color". that covers alot of ground. that pretty much means anyone who doesn't look european in origin. it's simpler than hashing out all of the ethnicities that make an american person. we'd have to go on forever just introducing ourselves. . . .