Pure black is easy: just die a bunch of times in body form (full HP).
To move tendency towards pure white, kill bosses, black phantoms, and help other people as a phantom. Generally speaking, you will reach pure white in all worlds if you kill the bosses and never die in body form. The easiest way to achieve that is to simply go back to the Nexus after every boss kill - because killing a boss automatically makes you regain body form - and kill yourself there. Then you can safely go through the next level in soul form.