Smoking paralyzes and damages cilia in the lungs, sinus, and bronchial passage. The main chemicals from cigarette smoke that have this effect are CO, Methane, and Arsenic.
The cilium in the bronchial passage are there to sweep particles that might enter the lungs, and within the lungs, they're there to sweep up mucus and foreign particles. There are really two types: motile cilia and non-motile cilia. The motile cilium sweep with a wavelike motion in one direction - moving junk out. The non-motile cilium are a kind of "sensory organ" that detect the foreign bodies and signal the production of mucus.
As they heal, they'll mostly begin working again. That said - inhaled nicotine still paralyzes them by itself to some far smaller extent, but you're not further coating them with a thick layer of "tar" or introducing the toxic gasses like CO, Arsenic, and Methane. As they begin working again, they'll do their jobs and sweep out the lungs, and you'll start coughing up the foreign matter that they should have dealt with in the first place.
Because of the paralysis, we have subjected ourselves to environmental pollutants like dust, dirt, airborne toxins, etc that would have otherwise been "stopped at the border" or dealt with over that period. Things that a non-smoker's lungs would have removed naturally, we've built it up over time. The mucus membranes will still encase the toxins, but we just don't have the facilities to remove them.
Cilium heal fairly quickly for the most part. The productive cough could start as soon as a few days, and last as long as 4-6weeks. If the cough is non-productive after a week or so and/or lasts longer than eight weeks, I'd strongly suggest consulting a physician.
The dead ones stay dead though, unfortunately, so the system will never again function at 100% efficiency...