All these responses have covered the main requirements. Every system is different. There are new installs and up-fitting of existing systems. The rules have changed over the years.
New systems can be either self-contained Ansul-type with a pre-wired control box and switches, or can be just fans mounted on ducts, and we have to wire everything together from scratch.
Sometines, there's already one or more shunt-trip breakers, sometimes a whole kitchen panel controlled by a shunt-trip. Often, only the exhaust fan was connected to the micros.
In existing systems, I use contactors; shunt-trips are expensive and require running a cable back to the panel. Contactors are easy, cheap, and can be mounted where needed.
Here's a few pics from a new church kitchen I didn't wire, but I installed the system:
The box contains four contactors. There were four 120v receptacles, so I used two 2p contactors for those. The three cables with the tape (a 12/3 and two 12/2's), are those feeds.
The fan supplies and loads (controlled by two 3p contactors), plus the circuit/light supply, enter and exit the top. From the bottom are the cables to the gas valve and the lights.
The 1/2" flex goes in the wall to the switches, and the 1/2" EMT to the horn-strobe, to the extinguisher box which contains the microswitches, and then on to the gas reset box.
Here's a pic of the wiring diagram:
Both of these circuits were fed by the same supply; I just showed them separated them for ease of tracing. (Big! Sorry.)
Now, under-hood lights must also shut off. Appliances under the hood that must shut down, whether their supply is under the hood or not. Unused receptacles can be blanked off.
We also have to install a horn/strobe unless there's a building alarm system tie-in, and a gas valve w/reset box that must shut down the gas even upon manual exhaust shutdown.
That means every morning starts with turning on the exhaust, pressing the button on the reset box, and then lighting each standing pilot. The owners and cooks HATE this requirement.