Expect the technician to ask about your fuel, the age of the equipment, and what happened just before it stopped. On an oil system they'll often check the nozzle, filter, ignition, and safety controls; on gas, the igniter, flame sensor, pressure switch, and venting. Some older Duxbury homes keep the boiler in a tight basement or crawl space, so clear a path and have a light ready.
Not every fix finishes on the first visit. If a part has to be ordered, ask what temporary steps can keep the house above freezing in the meantime. If the equipment must be replaced, gas piping changes go through the Building Department's plumbing and gas inspector, while oil burner and tank work falls under Fire Department permits.
After any storm flooding, a careful contractor will want the electrical side checked before restarting, and may recommend replacing controls that sat in saltwater rather than drying them out.