Expect the technician to check ignition, the flame sensor, the blower, the condensate drain on high-efficiency models, and the venting, then measure how the furnace is burning. A good visit also looks at the heat exchanger and the duct connections near the unit, since cracks and leaks there matter for safety and comfort.
Replacement involves town permits. Gas furnace work falls under the Building Department, which enforces the State Plumbing and Gas Code, has a Plumbing and Gas Inspector on staff, and offers online permitting; oil furnace work also needs the Fire Department's permit. If you'd like to check on a permit yourself, the Building Department stays open until 6 p.m. on Mondays and closes at noon on Fridays.
For oil and propane homes, a replacement visit may include options beyond another furnace, such as a high-efficiency oil unit, propane, or a heat pump, since a gas hookup isn't currently available through MGED.