Currently running one and somebody asked so I figured I'd do my best to throw together some simple but concrete things:
-Choose a place and a time you know as well or better than your players
I once got to say "Actually, I've been to Pollock's Toy Museum and it's fucking tiny and the coat check is right next to the entrance" instead of looking stupid when running Night's Black Agents for Ken Hite. Though I did pretty much rip the system into shreds accidentally kind of constantly but whatever that's another story.
-Figure out how much spy stuff you want the players to have and how hard you want it to be for the players to get it
One of the nice thing about Night's Black Agents for one-shots is you spend no time shopping, and even though I run my own games using a modified Call of Cthulhu (basically using the NBA skill list) the point is you want to have a clear handle on how the parent government or patron's largesse is going to shape the adventure. Technically the CIA could always call in an airstrike, and that could be boring. You need to carefully calibrate how you want to use the system and scenario to decide how much recourse the players have to crazy tech that can solve their problems before they come up.
-Get comfortable with how spy pacing is distinctive
Ok, in a super-hero game, you can run a 2-hour session of which an hour and a half is one fight with one villain and not only is everybody happy but that pretty much can be an average session. A little drama--biiiiiiig fight, lots of powers, done. Satisfying. That's why superhero games are pretty easy to run. Similarly, D&D games can typically be paced out to like a series of 5-10 moments of opening doors or entering hexes or encountering NPCs and then dealing with some unexpected consequence.
In a spy game, the unit of "something happened" is basically each time the players get concretely closer to their goal or some other major confrontation. That is a "beat" in a spy story. I roll successfully to see if I can detect a pattern in Worthington's tax returns over the years--beat. I talk to the bartender and he makes me as IRA and waves me off. Beat. Get comfortable with that--let the players enjoy the little world you're creating with these details. Make that as fun as the rooftop gunfight you know is coming.
-The spy equivalent of the dungeon is the heist
And I don't mean in structure, I mean in terms of reliably providing a session's-worth of reliably spyish activity. You name a target, a time, a place, and tell the players they need to steal, assassinate, kidnap, rescue or neutralize it. The rest is up to them.
It sounds preposterously simple but trust me, it works. Here's a freebie. They'll spend a half hour or more planning, they'll get in, they'll fail one crucial roll and the consequences will provide the fuel for the rest of the night.
-Hunter/Hunted is a good one to have in your pocket
"What if there's a crucial clue the players miss?"
"Oh just use GUMSHOE! Or the three clue rule! They'll never miss a clue again!"
Screw that, let your players deal with the consequences of their appalling incompetence. It's good clean fun and a plot structure so tight it's hard to think of a spy story that doesn't use it. Here.
In yesterday's game I told False Patrick that the cell data he Traffic Analyzed revealed:
-One number that gets called all the time
-One number that calls the target, only after they've consulted that first number
-One number that gets called the same time every week for 20-30 minutes
Patrick looked at the 3rd number and went "That's probably just his mom". And I was so happy--not because I'd fooled him, but because he had guessed exactly right. In the years he played in my games he'd gotten used to the idea that just because there's a detail doesn't mean it's important. Only hack GMs only give players details that turn out to be meaningful later.
-Enemies are whatever
Opposed NPC stats can be just average people 90% of the time with like one good stat and 1 skill. You don't even have to write them up ahead of time if you have a good handle on who they are. In most spy (and horror) systems, PCs are fragile enough that regular people with guns are quite enough to make a genuinely frightening combat.
The final boss can have stats, but even just an interestingly exotic place to fight and a lot of hit points or a bullet-proof vest results in a memorable encounter.
-You don't have to invent plot twists right up front
In making a D&D setting I recommend running that first adventure, then extrapolating the setting from what happens there. It worked for Tolkien (you got a....ring? Ok, let's see where the ring came from...). Run the first adventure, figure out what kind of PCs the players made and what kind of stuff you had to pull out of the hat that day to make the game happen. Then develop the plot twists out of that between sessions. As more and more elements come into play (one player is CIA one is MI5, you can do inter-agency rivalry, none of the players speak any other languages--give them an unreliable translator, etc). The twists will come organically once you get your feet on the ground in the world. Just character creation for 4 people alone will generate enough question marks to build plot out of for weeks.
-In other words, relax
I am making this sound easy, but it some ways, it kind of is. You don't have to genuinely scare people, like in horror, you don't have to invent some new exotic traps or weirdness, like in D&D, you don't have to make your villains seem as vivid as real comic book villains like in a superhero game, you just have to make this slightly alternate take on reality feel real. The spy genre is about how mystery and danger are hidden in banal objects--the bomb in the apple, the elevator with the frayed cable, the Man Who Goes Through The Blue Door--luxuriate in these details and other lives. Rushing toward set pieces isn't necessary--these players want to spy on things, let them.
And if that doesn't work, like Chandler said, just have some dickhead show up with a gun.