Verses of Sujud al-Tilawah in the Quran
Question

I would like to know the specific verses in the Quran where we should offer sujud al-tilawah (prostration of recitation).
Praise be to Allah.Sujud in the Quran
There are fifteen places in the Quran where we should perform sajdat al-tilawah (prostration of recitation) when reciting them. 
‘Amr ibn al-’As narrated that the Messenger of Allah (peace and blessings of Allah be upon him) recited to him fifteen verses in the Quran where one should prostrate, three of which are in al-Mufassal and two in Surat al-Hajj. It was reported by Abu Dawud, Ibn Majah, al-Hakim and al-Daraqutni, and classed as hasan by al-Mundhiri and al-Nawawi. 
Verses of sujud al-tilawah
The fifteen verses of sujud al-tilawah are:

Surely those who are with your Lord (angels) are never too proud to perform acts of worship to Him, but they glorify His Praise and prostrate before Him. [al-A'raf 7:206]
And unto Allah (Alone) falls in prostration whoever is in the heavens and the earth, willingly or unwillingly, and so do their shadows in the mornings and in the afternoons. [al-Ra’d 13:15]
And to Allah prostrate all that is in the heavens and all that is in the earth, of the live moving creatures and the angels, and they are not proud [i.e., they worship their Lord (Allah) with humility]. [al-Nahl 16:49]
Say (O Muhammad): Believe in it (the Quran) or do not believe (in it). Verily! Those who were given knowledge before it, when it is recited to them, fall down on their faces in humble prostration. [al-Isra 17:107-109]
When the Verses of the Most Beneficent (Allah) were recited unto them, they fell down prostrating and weeping. [Maryam 19:58]
See you not that to Allah prostrates whoever is in the heavens and whoever is on the earth, and the sun, and the moon, and the stars, and the mountains, and the trees, and al-dawab (moving living creatures, beasts, etc.), and many of mankind? But there are many (men) on whom the punishment is justified. And whomsoever Allah disgraces, none can honour him. Verily! Allah does what He wills. [al-Hajj 22:18]
O you who believe! Bow down, and prostrate yourselves, and worship your Lord and do good that you may be successful. [al-Hajj 22:77]
And when it is said to them: Prostrate to the Most Beneficent (Allah)! They say, And what is the Most Beneficent? Shall we fall down in prostration to that which you (O Muhammad) command us? And it increases in them only aversion. [al-Furqan 25:60]
[As Shaytan has barred them from Allah's Way] so that they do not worship (prostrate before) Allah, Who brings to light what is hidden in the heavens and the earth, and knows what you conceal and what you reveal. [al-Naml 27:25, 26]
Only those believe in Our ayat (verses, signs, etc.) who, when they are reminded of them, fall down prostrate, and glorify the Praises of their Lord, and they are not proud. [al-Sajdah 32:15]
And Dawud guessed that We had tried him and he sought forgiveness of his Lord, and he fell down prostrate and turned (to Allah) in repentance. [Sad 38:24]
And from among His Signs are the night and the day, and the sun and the moon. Prostrate not to the sun nor to the moon, but prostrate to Him Who created them, if you (really) worship Him. [Fussilat 41:37, 38]
So fall down in prostration to Allah, and worship Him (Alone). [al-Najm 53:62]
And when the Quran is recited to them, they fall not prostrate. [al-Inshiqaq 84:21]
Fall prostrate and draw near to Allah! [al-’Alaq 96:19] (See Fiqh al-Sunnah by Sheikh Sayyid Sabiq, 186-188)

Scholarly views of the narration of ‘Amr ibn Al-’As about sujud al-tilawah
Al-Albani said, in Tamam al-Minnah (296):
On the contrary, the hadith is not hasan, because it includes two majhul [unknown] narrators. Al-Hafiz said in al-Talkhis, after quoting the opinion of al-Mundhiri and al-Nawawi that it is hasan: ‘Abd al-Haqq and Ibn Qattan classed it as da’if [weak]. It includes ‘Abd-Allah ibn Munayn, who is majhul, and the one who narrated from him is al-Harith ibn Sa’id al-Atqi, who is also unknown. Ibn Makula said: He did not narrate any hadith apart from this one.”
Hence al-Tahawi was of the opinion that there is no second sajdah in Surat al-Hajj, towards the end of the surah. This is also the opinion of Ibn Hazm who said in al-Muhalla:
“Because it is not narrated in any sahih report that this was the Sunnah of the Messenger of Allah (peace and blessings of Allah be upon him), and there is no scholarly consensus to this effect. But it was reported with a sahih isnad that ‘Umar ibn al-Khattab, his son ‘Abd-Allah and Abu Darda performed sajdah in (the second verse quoted from Surat al-Hajj).”
Then Ibn Hazm discussed whether the sajdahs for the other verses quoted are prescribed in Islam. He mentioned that the scholars are agreed upon the first ten, that performing sujud when reciting these verses is prescribed.
 Al-Tahawi also reported this consensus in Sharh al-Ma’ani (1/211), but he said that the sajdah in Surat Fussilat was prescribed, instead of the sajdah in Surat Sad. 
Both scholars narrated ahadith with sahih isnads from the Messenger of Allah (peace and blessings of Allah be upon him) concerning the sajdahs in Sad, al-Najm, al-Inshiqaq and al-’Alaq. These last three are from the Mufassal, which is referred to in the hadith of ‘Amr mentioned above.
In conclusion, even though the isnad of the hadith is weak, it is supported by the consensus of the ummah which supports most of it, and by sahih ahadith which support the rest of it, except for the second sajdah in Suat al-Hajj, for which there is no evidence in the Sunnah or in the consensus of the scholars. But some of the Sahabah used to prostrate when reciting it, which could be taken as evidence, especially since no one is known to have disputed with them in this regard.
To sum up, the prostration of recitation should be performed when reciting the fifteen verses quoted above. 
And Allah knows best.