On an oil system, the technician usually starts at the tank and works toward the flame: fuel level, filter, line, pump, nozzle, ignition, and the flame sensor or cad cell. On propane or Eversource gas equipment, they'll check supply pressure, the igniter, and the safety switches. Either way, expect a combustion check before the system is left running.
Many Rochester houses sit well back from the road on large lots, so give clear directions, mention a long or unplowed driveway, and turn on an outside light if it's dark. Know where the basement entrance and the tank are before the contractor arrives.
If the fix is a part swap, the system may be running again on the first visit. If the burner or the appliance has to be replaced, oil burner work needs a Rochester Fire Department permit and gas or propane piping needs a permit through the town's Building Department, so expect a temporary repair or a follow-up visit.