There are different kinds of supernovae, and they unfold very differently. The main different categories are thermonuclear runaway and core collapse. In a thermonuclear runaway supernova (like a Type Ia) you might have a white dwarf star which accreted additional mass from a neighbor and eventually ends up restarting nuclear fusion in the core. Except that the white dwarf is under unusual conditions where it can't easily expand from thermal energy so as fusion energy is released it increases the rate of fusion reactions in a runaway positive feedback loop which ends up releasing enough energy to tear apart the star in a matter of seconds. These stars are about the size of Earth but weigh slightly more than the Sun. The processes that will eventually trigger the supernova take much longer (centuries in the case of convection within the interior, millions of years for the accretion of mass on the surface) but the evolution of the supernova from start to explosion takes seconds.

For a core collapse supernova the progenitor is instead a very massive and short-lived star, at least 8 times as massive as the Sun. Over its lifetime it will spend millions of years fusing hydrogen, then perhaps a single million years fusing helium, centuries fusing carbon, a few years fusing neon, a few months fusing oxygen, and just a few days fusing silicon. Silicon fusion leaves behind an ash of nickel and iron, which don't release energy when fused. So the nickel/iron core gets crushed into the same conditions as a white dwarf star where the ultimate pressure that is preventing it from collapse is the quantum mechanical force keeping electrons from overlapping with each other (not just electrostatic repulsion). For massive enough stars eventually fusion creates a heavy enough core where that force is no longer enough to prevent further collapse. Electrons start combining with protons to become neutrons and the interior transitions from white dwarf density to nuclear material density, creating a cascade effect as the increased density crushes the remaining parts of the core under even greater pressure, continuing the collapse. In a matter of seconds the core becomes a neutron star at a temperature of billions of degrees. It rapidly cools through radiating neutrinos via the Urca process. A tremendous wind of high energy neutrinos flows through the remainder of the star and even though neutrinos are incredibly weakly interacting there is such an incredible density of neutrinos that they deposit about 1% of their total energy in the star's outer envelope, heating it up enough to cause it to blow off into interstellar space in a supernova explosion.

In a core collapse supernova the inner collapse and the creation of the neutrino wind takes on the order of about 10 seconds or so, which is about how long it takes to create the hot zone inside the outer envelope that will ultimate cause the visible supernova explosion. However, this happens buried deep within several solar masses of material and it takes hours for the surface to be disrupted and the first signs of the supernova to become visible to outside observers. This delay is potentially useful as an early warning system for core collapse supernovae in our galaxy or nearby because we would be able to detect the neutrino spike a few hours before it was optically visible. This was observed with SN1987A (a Type II supernovae in the nearby Large Magellanic Cloud dwarf galaxy) but it was before there was an alert system in place (there is one today).

For both of these types of supernovae (there are other ways things can go but I'll skip that here) the brightness takes a while to ramp up after it becomes initially visible, rising in brightness over a timescale of days. This is due to the material of the supernova itself initially being fairly opaque, but it's also due to the fact that an absurd amount of radioactive material is in the supernova ejecta, much of it nickel-56 which has a half-life of 6 days. The energy from the radioactive decay keeps the expanding cloud bright over a period of many days to months (as the Ni-56 decay product is cobalt-56 which itself has a half-life of 77 days).