How to Do Sujud al-Tilawah
Question

Is it necessary to have wudu in order to do sujud al-tilawah (prostration required when reading certain verses of the Quran)? Do we have to say Allahu akbar when going down and coming up, whether that is whilst praying or otherwise? What should be said in this prostration? Are the du`as that have been narrated for it sahih? Is it prescribed to say salam after this prostration if it is done outside of prayer?
Praise be to Allah.Do you need wudu for sujud al-tilawah?
It is not essential to have wudu for sujud al-tilawah , according to the more correct of the two scholarly opinions. 
How to do sujud al-tilawah
There is no salam or takbir when coming up from sujud al-tilawah, according to the more correct of the two scholarly opinions. 
It is prescribed to say takbir when prostrating , because evidence to that effect is proven in the hadith of Ibn ‘Umar (may Allah be pleased with him). 
But if the sujud al-tilawah is done during prayer, then it is obligatory to say takbir when going down and when coming up, because the Prophet (peace and blessings of Allah be upon him) used to do that in every movement of the prayer, and he said: “Pray as you have seen me praying.” (Narrated by al-Bukhari in his Sahih, 595)
What to say in sujud al-tilawah
The same dhikr and du`as are prescribed in sujud al-tilawah as in the prostration during prayer, because of the general meaning of the hadiths concerning that. Among these du`as are: 
Allahumma laka sajadtu wa bika amantu wa laka aslamtu, sajada wajhi lilladhi khalaqahu wa sawwarahu wa shaqqa sam’ahu wa basarahu bi hawlihi wa quwwatihi, tabarak Allahu ahsan al-khaliqin (O Allah, unto You I have prostrated and in You I have believed, and unto You I have submitted. My face has prostrated before Him Who created it and fashioned it, and brought forth its faculties of hearing and seeing by His Might and Power. Blessed is Allah, the Best of creators). 
This was narrated by Muslim in his Sahih, 1290 from the Prophet (peace and blessings of Allah be upon him); he said that he used to say this dhikr during the prostration of prayer, according to the hadith of ‘Ali (may Allah be pleased with him). 
We have mentioned above that it is prescribed to say the same in sujud al-tilawah as in the prostration in prayer. It was narrated that the Prophet (peace and blessings of Allah be upon him) used to make du’a when he did sujud al-tilawah, and he would say:  
“Allahumma ‘ktub li biha ‘indaka ajran wa’mhu ‘anni biha wizran waj’alha li ‘indaka dukhran wa taqabbalha minni kama taqabbaltaha min ‘abdika Dawud (O Allah, record for me a reward for this (prostration), and remove from me a sin. Save it for me and accept it from me just as You accepted it from Your slave Dawud).” (Narrated by al-Tirmidhi, 528)
What is obligatory is to say “Subhana Rabbiy al-A’la (Glory be to my Lord Most High), as is obligatory during the prostration of prayer. Any additional du’a or dhikr is mustahabb. 
Is sujud al-tilawah obligatory?
Sujud al-tilawah , whether during prayer or outside of it, is Sunnah, not obligatory, because evidence to that effect was narrated from the Prophet (peace and blessings of Allah be upon him), in the hadith of Zayd ibn Thabit and in the hadith of ‘Umar (may Allah be pleased with him). 
For more, please see these answers: 32750 , 73402 , 131299 , and 4908 .
And Allah knows best.