Is the ignition a short event -- how long does it take? In other words, is there a sharp boundary between a "dense cloud, not yet a star" and a "young star"?

It takes a while, although it's relatively short compared to a star's lifetime -- about ten million years for a solar-mass star, followed by a longer period as a young star that's still gaining energy from gravitational collapse. Higher-mass stars form faster, but I wouldn't expect even the heaviest to form on human timescales.

A complication from an observer's perspective is that this sort of thing usually happens inside dense clouds which block out young stars in the visible spectrum. Most of what we know about star formation, we know because of observations at longer wavelengths.