Probably each Gamemaster runs debriefing in his own way, but here is a workable default template:
1. The entire team reports to the designated debriefing location, where the designated debriefing officer(s), typically the same high-clearance individual(s) who gave the team the original mission briefing, congratulate and/or condemn them for their performance. They take the Communication & Recording Officer's recordings and may take time out to review them. They may ask questions of the team leader and other team members (often the Loyalty Officer and the Communications & Recording Officer) about mission findings, untoward property destruction, etc.
2. The debriefing officer sends each team member into a confession booth or other isolated location, where The Computer or the officer quizzes the individual PC on salient mission points. The interrogation always includes inquiries about signs of treason or misconduct among the PC's teammates, and about inconsistencies between offered explanations and physical evidence.
Depending on circumstances and plausibility, this may be an opportune time for an individual PC's secret society to contact him and give him an IOU or other reward, or bust him down a couple of degrees.
3. The debriefing officer calls the entire team back together and offers his judgment of their overall and individual performance. He singles out individuals for approbation or condemnation, and he assigns rewards or punishments. If you wish, you can game this like a combat, using the Treason codes and the Universal Hostility System. Clearance changes are assigned on the spot and take effect IMMEDIATELY.
This is a good spot for the Gamemaster to hand out skill increases and other mechanical changes, too. Not that it will matter, because...
4. Did I mention the PCs still have their weapons? Somewhere in Step 3, they typically draw and start firing.
For excellent examples of Classic-style debriefings, see the many missions reprinted in PARANOIA Flashbacks. There are also some good debriefing scenes in Crash Priority.