Hawking radiation is a process that's always there when you have an event horizon. With black holes, the strength of this radiation is a function of its size: The heavier the black hole, and thus the bigger the event horizon, the colder the Hawking radiation.
While the strength of the Hawking radiation approaches zero as you go to larger black holes, it never actually becomes zero. So, in a sense, black holes are never truly black. They always radiate a bit, and they always slowly loose weight due to that radiation.
So, if you isolate a black hole from any incoming radiation, it will slowly shrink, and by shrinking it will become brighter, so it will shrink more rapidly in a self-amplifying process. This self-amplification is so strong, that any sufficiently small black hole looses all its mass within a finite time.
Wikipedia says:
So, for instance, a 1-second-life black hole has a mass of $2.28×10^5kg$, equivalent to an energy of $2.05×10^{22}J$ that could be released by $5×10^6$ megatons of TNT. The initial power is $6.84×10^{21}W$.
You see, a 300 ton heavy black hole is not black at all. Saying that it's white-hot is a severe understatement. It's so extremely bright that you just see a huge explosion that far exceeds the destructive power of all the worlds nuclear warheads taken together... And all this radiation is coming out of an object of subatomic size!
So, yes, black holes cease to be black as they shrink. Their Hawking radiation gives them the appearance of a perfectly black, more or less hot object. Big black holes are cooler than the cosmic microwave background, appearing as black as we can imagine. But smaller black holes glow with Hawking radiation. As the black hole shrinks, this glow goes all the way from a dim, reddish glow, over bright white light, brutally bright ultraviolet and deadly intensive X-rays to the destructive brightness of a nuclear warhead.
But all the time, it's just the Hawking radiation that you see. The singularity (or whatever happens to be within a black hole) remains shrouded behind the event horizon until the black hole has lost all its mass.