I have a Bryant 394 HAD with a fan that runs constantly. The thermostat is in the "auto " mode, and the burner shuts off properly to the thermostat setting. How do I correct this?

Some thermostats have a function that will keep the fan on all of the time. Check for that. If that's not the case, the thermostat may be faulty.

The circuit board in the furnace may be the culprit - either the fan relay contacts have fused together, or the fan timing logic circuit has failed. View circuit board by opening blower compartment and removing cover from board enclosure (if present). Disconnect wire from "R" terminal. If you see two "ice cube" relays on the board, tap on them with the butt of a screwdriver while holding in the blower door interlock switch. If blower stops, the contacts are fused. If not, the logic circuit has failed. Either way, replacement of the board will be necessary.