In series 12, The Master claims that he has
single-handedly destroyed Gallifrey
and later scenes in that series support this. Did we ever get any information on how this stunning achievement was made?
As of the end of season 12, the answer is no - we don't know how he did it.
All we know is that the Master selectively destroyed parts of it, so it cannot have been some weapon of mass destruction:
"I burned the Citadel".
"I destroyed a lot of things, but not this trove of secrets".
And of course, he didn't 'destroy' the Time Lords - he kept their bodies frozen. Time Lords cannot regenerate if their bodies are completely destroyed, so we would have to presume that he 'killed' them, or froze them alive before be burned places down.
Most importantly to note is that, after learning that Gallifrey had been destroyed, The Doctor apparently visited the planet several times trying to figure out what happened. She did not manage to ascertain that it was The Master, nor did she discover the preserved Time Lords - these things were only revealed to her by The Master in the final episode of the series. There were no other pointers as to how it happened before this.