Check the chimney from inside the fireplace to ensure the damper is open all the way. Shine a flashlight up the chimney and look for obstructions such as bird nests. Check the sides for an excessive buildup of creosote. Climb up a ladder and clean the chimney with a brush if necessary. If applicable, inspect the spark screen on the chimney cap to ensure it's clear. All these blockages can prevent the smoke in the fireplace from drawing upward.
Crack a window open in the same room the fireplace is in to assist the draw. This will allow air into the room to help provide air to the chimney.
Light a candle. Hold it up into the fireplace. If the smoke rises up the chimney, you have a good draw. If the smoke blows into the room, there's still a downdraft in the chimney.
Check the air pressure in the house. Negative indoor air pressure will cause a downdraft in the fireplace. Open a window or door in the downstairs. Wait a few minutes. Turn the furnace off, or, turn a fan off, if you have one. Wait a few more minutes for the air pressure in the house to stabilize. Close any skylights, as well as upstairs windows. Wait a few minutes then check the draw in the fireplace again with the candle.
Put on a pair of gloves to protect your hands. Roll up a newspaper to make a torch to fix the draw in the fireplace. Light one end of the newspaper and hold it up into the fireplace chimney. After the first one burns down, repeat the process with four or five or 5 more newspapers. These torches will provide warm air to clear the cold air blockage. They act like a siphon to get the air moving upward.
Light a fire in the fireplace. The smoke should rise upward and out the chimney as normal. Once the fire is established, close the window in the room.