Expect the contractor to start at the thermostat and power supply, then work through ignition, fuel delivery, and venting. On an oil system that usually means the nozzle, filter, and electrodes; on a gas system, the igniter, flame sensor, and pressure switch. They should explain the cause before they quote the fix.
Ask whether the repair needs a permit; replacing a whole furnace or boiler generally does. In Sharon, gas work goes through the Building Division's plumbing and gas inspector, who inspects by appointment on Monday, Wednesday, and Thursday afternoons, and an oil burner replacement uses the fire department's Oil Burner Installation Permit form. If heat has to be restored before the inspection, ask the contractor how they handle that.
After a flooded basement, a careful contractor will want to inspect every component that sat in water before restarting anything. Some controls and gas valves have to be replaced rather than dried out, and the contractor should tell you which.