how does an ansul system is wired?
The typical requirements are, as stated above, that the exhaust fan must turn on (called night mode) or stay on, the make-up fan must shut off or stay off, lights and gas and/or electrical equipment under the must shut off, and a horn/strobe or a building alarm must sound.
The ones I do are usually updating to existing systems, so there's no one way to wire them. Some have only exhaust, some have both make-up and exhaust. Some have gas appliances (which require a solenoid-valve reset box), some have electric, some have both.
Around here, the gas must shut down even with manual exhaust shut-off, which means relighting standing pilots every morning (and customers hate), although I have recently done a couple with a thermostat on the hood, and a couple with a low-presure bypass.
The systems we see have two SPDT micro-switches in the control box for us to use to make everything above happen. No connections can be made in the box, so a junction box must be mounted close by, and typically connected to the box with 1/2" FMC for the wires.
In smaller hoods, the motor(s) may be 120v, and most micros can control them directly. (After all, they're not used for daily operation.) In most larger hoods, they'll be 240v and/or 3 phase, requiring contactors that get switched the same way. The lights are only 120v.
If the appliances are already fed from shunt-trip breakers, or from a panel with a shunt-trip main, you only need to give them a voltage to trip. If not, you either need to install them, or use contactors (or a panel cvontrolled by a contactor) to shut them down.
Also, there may be one switch for both make-up and exhaust, or separate switches. Larger hoods may have more than one of each fan, and may be controlled by one, two, or more switches. I did one a couple of years ago that had two make-up and two exhaust switches.
how many circuits do I need?.
Again, it depends on the equipment installed. For the control wiring, one circuit is enough, and often supplies the lights as well. To give any more help, I'd need to know the details of each motor, appliance, etc.
This isn't something you want to do if you're not 100% sure about what is involved. Life safety and property damage are at risk from a fire, and there are reasons the requirements are there to minimize the danger.