I found the introduction a strange way to encouraging people to go for Refuge, i.e., on the basis of a "human situation is similar to an iceberg"; since this is going to Refuge on the basis of ignorance or blind faith.
In my reading of the Pali scriptures, generally people go for refuge for reasons such as a clear awareness of their personal suffering or dissatisfaction or in their clear awareness of the virtues & liberation of the Buddha.
For those cognizant of their own suffering & dissatisfaction, the Buddha pointed to craving & attachment as the causes of that suffering and pointed to the Noble Eightfold Path as the method to develop mental tranquility & liberating insight.
In short, it is self-clinging that causes suffering. If you are suffering, you should be able to see it is the mind's own selfishness, self-obsession, possessiveness, etc, that is causing & manifesting the suffering.
Further, the article is confusing because it gives the impression the 'self' creates desires and desires create perceptions.
In reality, ignorance & feelings condition perceptions, which in turn condition desires, which in turn condition attachment & the sense of "our self". That is why the Buddha called feelings & perception the 'citta sankhara' or 'mind conditioner' (MN 44).
The "self" does not create desires. It is desires that create the "self". It is feelings of pleasure & pain that create desires. The Buddha made this reality very clear in the Phagguna Sutta, in the Parileyyaka Sutta & in many other places.
Imagine a small new born baby. The baby has has no idea of 'self'. It has no concrete perceptions. A new born baby is an organism subject to the painful feelings of hunger & discomfort. From these painful feelings of hunger & discomfort come primal desires for relief. The parents of the child feed it food & give it comfort, from which the mind of the child experiences pleasant feelings. From these pleasant feelings it develops perceptions of "milk is good", "breast is good", "mother is good" and, eventually, as its brain/mind matures, perceptions of "my mother" & my father".
Therefore, the original source of perception is painful & pleasurable feelings rather than desire.
Attempting to see through the "deception of the self" is a difficult way for a novice to approach the path. This is similar to attempting to climb a tree from the top.
"Self" is certainly a deception however the path begins by seeing the deception of desires (in that worldly pleasures cannot bring lasting & true happiness). If the mind cannot see the deception of worldly pleasures & desires, it will struggle to develop the clear concentration (samadhi) meditation which serves as the basis for the insight meditation (vipassana) that can see through the deception of the illusory 'self'.
In short, when the mind is clear, it can start to examine the arisings & nature of the 'self' thoughts. There is actually no special method. One must simply meditate in quietude & stillness.