Tohe act of spotting pursuers and throwing them off in a way that would appear accidental, wa is known as “dry-cleaning” (“proverka” in Russian), in intelligence parlance.

Since a target who was obviously under close watch was likely to be a trained intelligence operative, their demeanour must not arouse suspicion.

As a KGB trainee, Oleg would learn how to set up a "signal site"," how to make a “brush contact,” and how to make a “dead-letter drop”.”

A "signal site" consisted inof leaving a secret sign in a public place that meant nothing to a casual observer, but would convey to a spy a rendezvous message to a spy.

"Consisted of" is the correct phrase. :)

A “brush contact” consisted inwas the ability to physically passing a message or item to another person without being spotted.

A “dead-drop letter” consisted inof leaving a message or cash at a given spot to be picked up by another without making direct contact.

The aim was to arrive at the rendezvous* location spotlessly “dry-cleaned” to drop off or pick up information in complete securitely.

When they were absolutely sure to have gone “black”—" (western intelligence parlance for being undetected—), they would eventually approach the given spot.

These were highly-trained agents in the surveillance field, which wasunder the responsibility of KGB’s 7th Directorate.

At the end of each test, the students and the surveillance team would compare notes.

Proverka was nerve-racking, and both physically and mentally exhausting.

*is "rendezvous" enough to mean the "meeting" place or is necessary to say "rendezvous' spot"?

I would use "rendezvous spot" (or location, place, etc.).

To spot pursuers and throw them off in a way that would appear accidental, was known as “dry-cleaning” (“proverka” in Russian), in intelligence parlance.

Since a target who was obviously under close watch was likely to be a trained intelligence operative, their demeanour must not arouse suspicion.

This is a little unclear to me. Whose demeanour is referred to here? The target's? And what do you mean "obviously under close watch"? Obvious to whom?

As a KGB trainee, Oleg would learned how to set up a "signal site", how to make a “brush contact” and how to make a “dead-letter drop”.

I am not sure about this, but it seems awkward to use "would learn" here while the rest of the text is in past tense

A "signal site" consisted in leaving a secret sign in a public place that meants nothing to a casual observer, but would convey to a spy a rendezvous to a spy.

These were highly-trained agents in the surveillance field, which was the responsibility of KGB’s 7th Directorate.

At the end of each test, the students and the surveillance team would compare notes.

Proverka was nerve-wracking and physically and mentally exhausting.