Reciting the opening du’aa’ in taraaweeh prayers
Question

                Should we read the opening du’aa’ at the beginning of each two rak’ahs of taraaweeh prayers?.
Praise be to Allah.Yes, it is prescribed for you to recite the opening du’aa’ at the beginning of each two rak’ahs of taraaweeh prayer, and other naafil prayers, because of the general meaning of the evidence. 
With regard to the opening du’aa’ in qiyaam al-layl in particular, the following words were narrated: 
Laa illaha ill-Allaah (three times), Allaahu akbar (three times), Allaahu akbaru kabeera wa alhamdu Lillaahi katheera wa subhaan Allaahi bukratan wa aseela (There is no god but Allaah, Allaah is most Great, Allaah is most Great, much praise be to Allaah and glory be to Allaah at the beginning and end of the day).” A man from among the Sahaabah started his prayer with these words and the Prophet (peace and blessings of Allaah be upon him) said: “I was surpised, the gates of heaven have been opened for these words.” 
“Al-hamdu Lillaahi hamdan katheeran tayyiban mubaarakan fihi (Praise be to Allaah, much good and blessed praise).” Another man started his prayer with these words and the Prophet (peace and blessings of Allaah be upon him) said: “I saw twelve angels competing to see which of them would take these words up.” 
“Allaahumma laka’l-hamd, anta noor ul-samawaati wa’l-ard wa man fihinna, wa laka’l-hamd anta qayyim al-samawaati wa’l-ard wa man fihinna, wa laka’l-hamd, anta malik al-samawaati wa’l-ard wa man fihinna. Wa laka’lhamd, anta’l-haqq, wa wa’duka haqq, wa qawluka haqq, wa liqaa’uka haqq, wa’l-jannah haqq, wa’l-naar haqq, wa’l-saa’ah haqq, wa’l-nabiyyoon haqq, wa Muhammad haqq. Allaahumma laka aslamtu, wa ‘alayka tawwakaltu, wa bika aamantu, wa ilayka anabtu, wa bika khaasamtu, wa ilayka haakamtu. Anta rabbunaa wa ilayka al-maseer, faghfir li ma qaddamtu wa ma akhkhartu, wa ma asrartu wa ma a’lantu, wa ma anta a’lam bihi minni, anta’l-muqaddim wa anta’l-mu’ukhkhir, anta ilaahi, laa ilaaha illa anta wa laa hawla wa laa quwwata illa bika
(O Allaah, to You be praise, You are the Light of the heavens and the earth and everyone in them. To you be praise, You are the Sustainer of the heavens and the earth and everyone in them. To You be praise, You are the Sovereign of the heavens and the earth and everyone in them. To You be praise, You are the truth, Your promise is true, Your words are true, the meeting with You is true, Paradise is true, Hell is true, the hour is true, the Prophets are true, Muhammad is true. O Allaah to You I have submitted, in You have I put my trust, in You I have believed, to You I have repented, with Your help and guidance I have debated, and to You I turn for judgement. You are our Lord, unto You is our return. Forgive me for my past and future sins, for those I have committed secretly and those I have committed openly, and for whatever You know more about than I. You are the One Who brings forward and the One Who puts back, You are my God, there is no god but You, and there is no power and no strength except with You).” 
Allaahumma Rabba Jibreela wa Mikaa’eela wa Israafeel, faatir al-samawaati wa’l-ard, ‘aalim al-ghaybi wa’l-shahaadah, anta tahkumu bayna ‘ibaadika fima kaanu fihi yukhtalifoon, ihdini lima’khtulifa fihi min al-haqq bi idhnika, innaka tahdi man tasha’ ila siraatin mustaqeem (O Allaah, Lord of Jibreel (Gabriel), Michael and Israfeel, Creator of the heavens and the earth, Knower of the unseen and the seen, You are the Knower of the unseen and the seen, You will judge between Your slaves concerning that wherein they differ. Guide me to the truth of that wherein they differed by Your leave, for You guide whomsoever You will to the Straight Path). 
He used to say Allaahu akbar ten times, al-hamdu Lillaah ten times, Subhaan Allaah ten times, Laa ilaaha ill-Allaah ten times and astaghfir-Allaah ten times, and he would say, Allaahumma ighfir li, wahdini, warzaqni, wa ‘aafini (O Allaah, forgive me, guide me, grant me provision and keep me safe and sound) ten times. And he would say “Allaahumma inni ‘aoodhu bika min al-dayq yawm al-hisaab (O Allaah, I seek refuge with You from hardship on the Day of Reckoning) ten times, and “Allaahu akbar (three times), Dhu’l-malakoot wa’l-jabaroot wa’l-kibriya’ wa’l-‘azamah (Allaah is most great, Possessor of Sovereignty, Power, Magnificence and Might).” 
See Sifat Salaat al-Nabi by al-Albaani p. 94-95.