Divers had this problem dating back to the 1950's and the solutions were varied; from spit to rubbing with a cigar stub. These simple measures were generally all that was needed. Continuing until more recent years, no initial cleaning was needed, the diver just rubbed in some no fog or spit and jumped in. In the past decade, something has happened in the manufacture of glass which calls for more radical intervention including preemptive treatment of a new mask. Following that, if more than a spit wash is needed before diving something is wrong, the glass is still contaminated. Recently, I've been cleaning a new mask with Starbrite liquid rubbing compound. After this the mask is still dirty with residue from the compound so I use baby shampoo or other stuff like toothpaste to remove that. The mask is spit washed and rinsed under the faucett. Then, I exhale into the mask. A clean mask will show no fog or a tiny spot of fog somewhere at most. When the mask shows no fog the job is done. After that, at the beginning of the diver's day, a spit wash should be all that is needed for the life of the mask.
About the burning, I have heard this but not tried it.