When smoke damage appears on glass and mirrors, it can be nearly impossible to remove by standard means. A washcloth or paper towel will not pick up the sticky smoke residue properly and you will be left with smearing.
Spray your glass cleaner onto the glass or mirror that you want to clean. Make sure to saturate the surface. This will require using more glass cleaner than you normally do. If you miss spots, this may result in smearing.
Ball up your newspaper and wipe down the glass or mirror. You should use a copious amount of newspaper. When your newspaper becomes saturated with glass cleaner, throw it away and use a new sheet. You do not want your newspaper to get too wet, otherwise it will just move the glass cleaner around and not absorb the smoke residue.
Allow the glass or mirror to dry. You should notice an extreme improvement. For severe smoke damage you may need to repeat the process once or twice to give your glass or mirrors back their sparkling and clear shine.