Put on a dust mask and safety goggles to protect yourself from soot. Check the damper to make sure it's completely open. Use a bright flashlight to look up and inside the chimney for obstructions such as bird nests; clean out any you find. Check the flue above the damper to see if the chimney needs to be cleaned. Gently scrape the area with a fireplace poker. If the creosote is 1/4-inch thick or more, clean the chimney before you use it. Excessive creosote can restrict the air flow, as well as cause a chimney fire.
Check the windows in the upstairs of the house. Make sure they are closed tightly. Make sure the attic is closed off as well. Open a window in the room -- on the windward side of the house, if possible -- or an exterior door a few inches. This will add ventilation to the room. If there's a cold air return in the room connected to a forced-air heating unit, temporarily shut the furnace off so it's not pulling air out of the room.
Put on a pair of leather gloves. Roll a piece of newspaper up. Light it with a match and hold it up into the chimney. This will help warm the air to prime the chimney so an upward draft is created. You may need to do this several times until the smoke rises up successfully. Once it does, you can build a fire in the fireplace. Close the window or door, and turn the furnace back on.