How can we know that we experience sensations as a series of discrete sensations?

You have to do this by stages while practicing Satipathana. Just practice breath meditation first. Then practice some walking meditation. It is gradual training.

You could try to understand this by your own meditation experience, or you could trust science (for now).

From this April 2016 article in Quartz based on this research paper:

First, the authors argue, we unconsciously process visual stimuli continuously, and are oblivious to this stage. We only then become consciously aware of the information once it has been transferred to conscious perception, which happens in discrete moments, or “time slices.”

Michael Herzog, a professor at the École polytechnique fédérale de Lausanne’s Brain Mind Institute in Switzerland, and Frank Scharnowski, a cognitive neuroscientist at the University of Zurich, argue that we’re unaware of the gaps in our consciousness. They say there can be a 400-milisecond lag between unconsciously receiving stimuli and transferring it to conscious perception.

“We perceive time as continuous just as we perceive a line as continuous even though its ink is of discrete atomic nature,” the authors write in their paper.

But our perception of conscious does not align with reality. “According to our model, the output of unconscious processing is discrete, meaningful, and rendered conscious at once. Large parts of unconscious processing will never reach consciousness,” the researchers say.

The authors note that the debate over how consciousness works has a long history. In the third century BC, the Abhidharma Buddhist school put forward the theory that consciousness is made up of discrete moments. There are numerous more recent papers arguing for just such a conclusion. Meanwhile, experiments show that when two stimuli are presented in rapid succession, they’re perceived simultaneously, while discrete perception is thought to explain various visual tricks, such as the optical illusion that often makes spoked wheels look as though they’re moving in reverse, and flash lag illusion, where a flash that occurs in the same place as a moving object is perceived to be in a different location.

This April 2016 Science Alert article adds:

In other words, while we're taking the world in, we're not actually consciously perceiving it. Instead, we're just mutely using our senses to record data for up to 400 ms at a time. Then, in what could be called a moment of clarity, we consciously perceive the stimuli that our senses have detected.

The team thinks this presentation of information to our consciousness lasts for about 50 milliseconds, during which we also stop taking new sensory information in. And then repeat.

Our senses start taking new information in from whatever stimuli are around us, before handing it off to our consciousness to perceive and enjoy – back and forth, and so on, and so on.

The team says each window of recording and playback would last for a different amount of time, depending on the kind of information being processed.

While the constant to-and-fro suggests consciousness is anything but a seamless experience, if the researchers are correct, our brains somehow manage to stitch everything together so it feels like a continuous flow of events with no interruptions.

There is obviously not a continuous stream of sensations otherwise the mind could remember every sensation, similar to how every frame in reel of movie film can be viewed. In other words, the sensation experienced one second ago has disappeared, forever. To believe there is a continuous stream of sensation is to only observe arising & to not observe passing/disappearance. Its like a person given a box of delicious chocolates that hungrily can only see the next chocolate to be eaten, never realising each chocolate is disappearing & soon there will be no chocolates left, which eventually brings despair when the chocolates (similar to life) run out

Regardless, what Daniel is writing about, such as observing 40 sensations per second, is not found in the reported teachings of the Buddha, although it may possibly be found in later philosophy called Abhidhamma. To me, what Daniel is writing about is unimportant for clear insight, because objects must be very discrete to experience abrupt disappearance (rather than a blur of oscillating sensations the mind becomes infatuated with; like becoming infatuated with the oscillations or vibrations of a girl dancing on a cliff; rather than watching the girl fall off the cliff, to her death).

The Buddhist scriptures refer to observing the coming-to-be & then disappearance of a single in-breath, then an out-breath (MN 118) then, on a more advanced level, the arising, persisting & disappearing of a feeling, perception or thought (AN 4.41). This is more than enough for the purpose of vipassana. For example, merely observing a single breath, until it disappears; then observing the next breath, until it disappears, is enough to get started on seeing the true nature of life phenomena.

We are typically quite sloppy about what are physical sensations and what are mental sensations (memories, mental images, and mental impressions of other sensations). These two kinds of sensations actually oscillate back and forth, a back and forth interplay, one arising and passing and then the other arising and passing, in a somewhat quick but quite penetrable fashion. Being clear about exactly when the physical sensations are there will begin to clarify their slippery counterpart that helps create the illusion of continuity or solidity: flickering mental impressions.

If you can perceive one sensation per second, try for two. If you can perceive two unique sensations per second, try to perceive four. Keep increasing your perceptual threshold in this way until the illusion of continuity that binds you on the wheel of suffering shatters. In short, when doing insight practices, constantly work to perceive sensations arise and pass as quickly and accurately as you possibly can

How fast are things vibrating? How many sensations arise and vanish each second? This is exactly what you are trying to experience, but some very general guidelines can provide faith that it can be done and perhaps point the way as well. Begin by assuming that we are talking about one to ten times per second in the beginning. This is not actually that fast. Try tapping five to ten times per second on a table or something. It might take two hands, but it's manageable, isn't it? You could obviously experience that, couldn't you? That's the spirit! There are faster and slower vibrations that may show up, some very fast (maybe up to forty times per second) and some very slow (that are actually made up of faster vibrations), but let's just say that one to ten times per second can sometimes be a useful guideline in the beginning.

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Since I just used this dangerous phrase “the mind,” I should quickly mention that it cannot be found. I’m certainly not talking about the brain, which we have never experienced, as the standard for insight practices is what we can directly experience. As an old Zen monk once said to us in his extremely thick Japanese accent, “Some people say there is mind. I say there is no mind, but never mind. Heh, heh, heh!”