How far to open damper in fireplace?

To get the best and safest draft, open the damper all the way.

Your goal is to get good air flow out the chimney - you don't want it backing up into the room. That's why people get carbon monoxide poisoning: the damper was closed too much and the room filled with smoke and fumes while the fire burned down.

Always open the damper all the way when lighting the fire and keep it that way until the fire has completely burned out.

If the fire isn't hot enough, add more fuel. To maintain a consistent flow of heat after the fire is established, you may adjust the draft, but not by closing the damper. To reduce the flow of air into the firebox, partially cover the air vents with heat-proof aluminum foil.