I did a search and read all of the William Wallace stuff, but only a vague mention of him "brutally executed" was made. How exactly did they do it and how common was the form of execution? And how do we know for sure it happened this way?
William Wallace was hanged, drawn, and quartered, which was the official punishment for all men convicted of high treason at that time in England.
He would have been dragged to the execution site behind a horse, where he was hanged by the neck until almost dead. Then he would have been emasculated (had his genitals cut off), and disemboweled. His bowels (and possibly his genitals) would then have been burned while he was still alive. Then he would have been beheaded.
The head was preserved in pitch or tar and then stuck on a pike on London Bridge, and the body was quartered - cut into four parts - and the quarters were sent to Newcastle, Berwick, Stirling and Perth to be put on display as a warning to others.
This was the standard penalty for high treason, so it was used quite a bit. In fact, Wikipedia has a List of people hanged, drawn and quartered.