There are a few methods that can be imagined in regards to the "descent" of the Quran through revelation. They are enumerated as under:
First method: In this method the sayings of the Infallibles are used as a reference to prove that the Quran was sent down through revelation; that is, there are clear and decisive narrations from the Holy Prophet (pbuh) and the infallible Imams who said that the Quran was revealed by God. Given the miracles of the infallibles especially the Holy Prophet of Islam (pbuh) and in view of the fact that they are immune to any intentional and inadvertent errors (in action or saying) as discussed in its own appropriate place, the sayings of the infallibles are acceptable and serve as good proof. However, this method does not seem to be easy, effortless and free of any difficulty because firstly, the Prophet (pbuh) himself introduced the Quran as a miracle to prove his prophetic mission. Secondly, none of the miracles of the Prophet (pbuh) and the infallible Imams have lasted thus far except the Quran, though it has been proved through indisputable, concrete and indubitable evidence. In addition, such an argument is narrative and incompatible with what is intended here and is considered to be a theological criterion in the discussion. The criterion for theological issues is their being rational.
It is, therefore, necessary to be extra careful when using this method to demonstrate that the Quran was revealed by God and when dealing with the objections raised against this method.
Second method: In this method, the Quran itself is used as a reference to prove that it was sent down and revealed by God, the Exalted. He has times and again said in the Quran: "Surely We have revealed the Reminder and We will most surely be its guardian." "He has revealed to you the Book with truth." "This is because Allah has revealed the Book with the truth." "Had We sent down this Quran on a mountain, you would certainly have seen it falling down, splitting asunder." These verses of the Quran clearly indicate that the Quran has been sent down by God.
This above argument seems to be circular because the revelation of the Quran and its authoritativeness have not yet been proved so that we can turn to it and use it as a prelude to our argument. However, if we take a closer look at the verses, we can turn to the verses themselves to prove that the Quran was sent down through revelation.
It is worth mentioning that verse 23 of Chapter Al-Baqarah such as "And if you are in doubt as to that which We have revealed to Our servant, then produce a chapter like it" or other verses like "And if it were from any other than Allah, they would have found in it many a discrepancy"imply that the Quran has been sent down by Allah to mankind. However, since such verses refer to the miraculous feature of the Quran, they are not considered as a textual and Quranic proof; rather they are rational or external arguments that have also been used in the Quran itself. In fact, the aforementioned verses propose to the intellectuals and truth-seekers the third method for guidance which is completely rational.
Third method: The Quran's "descent" through revelation is proved by way of the miraculous feature of the Quran. This method which is the most common of methods studies certain features which are in the Quran and which imply that the Quran was revealed by God. 
Hadavi Tehrani, Mahdi, Theological Foundations of Ijtihad, Khana-e Kherad Cultural Institute, Qom, 1st edition, 1998.
 - Hijr:9 "انا نحن نزلنا الذکر و انا له لحافظون"Zikr in this verse has been interpreted as the Quran.
 - Aal-e Imran:4. "و انزل الفرقان"
 - Al-Baqarah: 176 and Al-Araf:196. "نزل الکتاب" The word Book refers to the Holy Scripture i.e. the Quran because Torah and the Gospel had been revealed before the Quran.
 - Al-Hashr:21 "لو انزلنا هذا القرآن..."
 - This verse challenges the unbelievers to produce the like of the Quran's verses.
 - Al-Baqarah: 23 "و ان کنتم فى ریب مما نزلنا على عبدنا فأتوا بسورة من مثله"
 - Al-Nisa: 82 "لو کان من عند غیر الله لوجدوا فیه اختلافاً کثیرا"
 - See: Index: The Miraculous Aspect of the Quran, Question 70 (site: 311).
 - Hadavi Tehrani, Mahdi, Theological Foundations of Ijtihad, pg.46-47.