Be sure the chimney is clean and in good condition. Be sure the damper is open before starting a fire. Don't burn trash in the fireplace. A screen or glass doors should cover the front of the fireplace to prevent sparks from flying out into the room. Seasoned wood is safer than green wood.
Hardwoods have less creosote build-up than softwoods.
Ashes should be removed into a metal container and allowed to thoroughly cool before being placed in the trash container. Don't leave small children alone in a room with a fire. Do not leave a fire burning when you go to bed or leave the house.