The thing is, they always use all three of them simultaneously. Push 'em all down to fade you out, and push them all up to fade you back in. Any treknobabble explanation needs to take that into account.
The used all three of them simultaneously *most *of the time, which makes perfect sense. 95% of the time, the transport goes through with no difficulty at all. But whenever there’s a problem with transmission, that’s when you see them fiddling around with individual levers.
There one episode in “TOS”- “Obsession” when Spock and Scotty are at the controls, trying to beam Kirk aboard before the anti-matter bomb goes off and Spock says “cross circuiting to B” which ultimately saves Kirk and the other person.
You have to pull down lever 2 when Evil Lincoln is trying to escape from the Holodeck.
If you align them wrongly . . . .
This is the drill:
You move all three levers together. Except when there’s trouble, then you look down at them, move them a bit, then look at the sparkles, then look at the levers again. Then you push a couple a little faster than the other.
If you really suck at this, Scotty or Spock will push you out of the way, and THEY will push all three levers together. Because they’re better at it than you are, even though you’re the transporter officer with special training. I’ll bet that makes you feel stupid, huh?
And if it’s beardy Spock and you don’t ‘compensate’ for ‘electrical disturbances’ by pushing the three levers together enough, you get aognized - with your own agonizer. That’s cold. But you deserved it. Years of transporter training, and you can’t move three levers in the proper sequence? You suck. And now as a result, you’ve got three total pussies on your planet-destroying starship, whining and moaning about peace and understanding. You fail at Star Trekking.
I’ve always wanted to meet the person who wrote the stuff that was listed in the screenplay as [TECH]
(The [TECH] marker was their shorthand for “Geordi will babble on excitedly for 25 seconds about why it won’t work.”)
The real reason though?
Of course, that only brings us to why did the original transporter have three controls? The console diagram in the Tech Manual describes them as “sequence initiators.”
Easy they are circuit A B and C.
You need redundancy when transporting people cause you never know they may have gold dust on them or an ion storm may be interfering or a giant space amoeba is sucking the power off your ship. Therefore when you are in a normal situation you use all three with power distributed evenly through the circuits until there is some malfunction. In that case (Which usually happens) the Transporter Chief or Chief Engineer or nosy knowitall Vulcan Science officer can switch to individual circuits diverting full power through that circuit to up the gain controls.
This usually ends up Resulting in two things…
- you save the guy you are beaming up and
- you blow the circuit out resulting in the Pad letting off a nasty sound and puff of dramatic smoke.
The later ships tried 5 and 6 circuit levers but only certain species could operate them with any efficiency and as Starfleet is a mostly racist organization there weren’t enough of those species in service for it to work.
I read somewhere that Levar Burton actually improvised most of that stuff - he was better at it than the writers.
Roll, Pitch, and Yaw.
There are. FOUR! levers!
If 25 years of Windows has taught us anything, this is it. 
Heat, Cool, Defrost.
The answer is obvious: red, green and blue. You need to beam all three colours together.
Sulu’s ship has four levers.
Oh, my!
Blue, Green, Red.
Or Cyan, Magenta,Yellow.
Depends on which color space you’re using.
You beam colors separately!
We’ve replaced Scotty’s usual transporter control levers with the decaying innards of a dead platypus. Let’s see what happens …
Kirk, staring at giant icecream cone: “Energize.”
Scotty: “Ewwwww!”
Kirk: “Gentlemen, beam me up!”
Spock" “Ewwwwww!”