To burn the accused.
I'm no authority, but here's how I remember it from the classes I took...
It would be entirely a church matter (as opposed to Common Law), so yes, some church official would preside- the more scandalous the matter, the more prestigious the official- unless they didn't want to get involved personally (perhaps if a noble was involved?)
Remember that around this time the Church had a LOT of RL problems, in the form of corruption, lack of reliable personnel, and an all-too-common loss of the greater goal. A long era of allowing anyone into the clerisy, with no screening and little oversight, coupled with a period of general suffering among the populous, and generations of such, led to many seeing the Church not as a holy calling, but a gravy train, a license to sin. Many could barely speak latin, had a weak grasp of doctrine, and the wide variety of corruption (see "cloth of gold", "butter towers", and any of the 7 deadly sins) led to such counter-movements as the Albigensians and various pauper sects. However, they did learn to cover their butts, and keep what little power/position they could claw up. (And even the good ones found themselves caught up in this morass, to their horror.)
Anyway, Politics played a huge role in who was in charge, and why, and who was accused and why. And that's Politics both internal to the Church, and external with regard to relations with the Nobles. So when we say "The Prosecution", often we are also saying "The Catholic Church" as a whole.
There was no Bill of Rights, so an attorney for the Defense was often non-existent or flat-out denied, or a purely perfunctory role, just someone acting as moral support while the drama went on its predictable course. Often, the Defense and the Prosecution were essentially one and the same, both assuming Guilt and working together toward a confession. Since it wasn't a common law issue, the presiding judge/bishop/cardinal/whoever, to a large extent, could make up the rules as they went along. Too much fun, really.
However, often noted scholars who were sympathetic to the Defendant would stand in as Defense, tho' sometimes at their own peril- too aggressive a defense could result in the defending advocate being charged with the same heresy!
Jurors, if any, were often "buddies of the church"- hand selected by the prosecution/judge/church because of their views and/or subservience to the Judge. Sometimes they were under scrutiny as much as anyone, for they found against the judge's opinion, that would "go down on their permanant record"- and that was a scary proposition. Last thing you wanted was to be associated with being soft on heresy, even if you were the counsel for the defense.
The defense, therefore, often did not try to defend the beliefs of the accused, but to "re-explain" them in a more acceptable light. That is, the defendant had to back out of their position without admitting it was heretical in the first place - "it was all a misunderstanding!"
Judges and jurors were, as a rule, not overly understanding of such.