How "fast" do astronomical events occur? I've seen quite a few news about astronomy but I'm not deep into knowing how it works or how people observe it. It got me thinking: if I want to watch a supernova for example, how long will I have to look for it to watch the whole "event"? Or events like NASA "seeing something coming out of a black hole", were they "looking" at the blackhole when something came out really quickly or did they observe it for months? Or maybe the birth of a blackhole?

Now, I do know black holes that quite a few trillion of years to vanish, I'm just curious how much time does it take for astronomers to observe such events.
A supernova (and many other interesting events) starts abruptly -- a flash of neutrinos lasting just a fraction of a second, but then different aspects of the event play out over minutes, days, hours or years.  The astronomy community has for some years been developing increasingly sophisticates ways to deal with such events early on. Instruments with a very wide field of view (gravitational observatories, neutrino observatories, gamma ray detectors on satellites) detect the events initially and bring first networks of robotic telescopes and then humans and still larger telescopes into the loop to try and get as much information as possible about the violent and fast developing early stages. See for example http://growth.caltech.edu/

Other things are slower. The "something coming out of a black hole" (not really that, just something coming from very close to a black hole) event takes a long time, this was just the first occasion when they'd observed that black hole with the right instrument.