Here’s pretty much all the pertinent parts of his article:

That said, the key to amphetamines and Ritalin is to stop thinking of them as stimulants, and to think of them as reinforcers.

Let’s conceptualize how these drugs work. Imagine getting a brain scan while you are performing a task. The parts of your brain you are using for the task will light up, brighter than those you aren’t using.

Now you drink coffee (1). The whole brain lights up brighter, proportionally.

Now you take amphetamines. The parts of your brain that you are using light up brighter, but the parts you aren’t using go darker. Get it? Caffeine is a global brain stimulant, while amphetamines focus your attention, reducing distraction.

This is entirely selective and controlled by you. You have to decide what you want to focus your attention on. If it’s reading, the reading parts of your brain will be brighter. But if you stop reading and decide to talk to your friend on the phone, you know, the hot one with the hotter roommate, then you’ll be more focused on that (obviously). Attention is always decreased when it is split among several tasks. In other words, you can only concentrate on one thing at a time, even though it may feel like you are doing two things at once.The power of amphetamines is this: you take them again, in the same dose, 30 minutes before your test.

In a metaphoric sense, taking the amphetamines during the test, under the same circumstances as you had been previously studying, will “remind” the brain of that context. If you see a question that “resembles” something you studied, your mind will be primed to recall it better.

Remember I said you can only concentrate on one thing at a time, that attention decreases when it is split? The trick here is to make everything about studying into one large “thing.”

Here’s an example: if you listen to a symphony, you will hear music. Musicians, however, hear both the music and every single instrument. They can attend to each instrument individually and simultaneously hear how each instrument fits into the larger context. A non-musician can’t do that. If he’s concentrating on the oboe, he doesn’t “hear” the violas.

Studying has to become a large symphony, everything doing its part correctly, expectedly. So on performance day (testing) you play the same symphony. You’re not trying to concentrate on each part, if you’ve practiced enough it should be second nature. The amphetamine helps facilitate this.