After doing a bit of research online, I finally found out how to light my basement wood stove without setting off the fire alarm. It all has to do with the basic principle that hot air rises and that colder, heavier air settles. When it's cold outside, the chimney of my wood stove is filled with cold, dense air pushing downward.

If I just put some kindling in the stove and light it and throw a log on, there isn't enough heat being generated in the beginning to push all the cold air upwards and out of the chimney and the smoke will instead pour back into the room. First you need to "prime" the chimney and reverse this airflow.

I threw several of copies of the free, local hippy newspaper into the stove and lit them first because newspaper burns hot and fast. A bit of smoke still poured into the room but after a few minutes the hot air started to rise up the chimney and push the cold air out and I had achieved sufficient outward airflow, enough to throw a log on and let it burn without smoking up the entire room. Science!

Next time I light the stove, I might try blowing a hairdryer up the chimney for a few minutes to see if that works to reverse the airflow. That way I can light the stove without any smoke blowing back into the room at all.