Dua before reciting the Holy Qur'an .It has been narrated that Imam Ja`far al-Sadiq (a.s) used to say the following supplication before he would start reciting the Holy Qur'an
wa kalamuka alnnatiqu `ala lisani nabiyyika ja`altahu hadiyan minka ila khalqika wa hablan muttsilan fima baynaka wa bayna `ibadika
(these are) Thy Words, Thy Prophet gave tongue to, (whom) Thou appointed as a Guide for the people, and an uninterrupted closely connected link of protecting friendship between Thee and Thy servants.
allahumma inni nashartu `ahdaka wa kitabaka allahumma faj`al nazary fihi `ibadatan wa qira‘aty fihi fikran wa fikry fihi a`tibaran
O Allah I make publicly known Thy testament and Thy Book. O Allah let me pay full attention to (this) adorable pious work; let me notice and take warning from (this)thoughtful reflection;<
wa la taj`al qira‘aty qira‘atan la tadabbara fiha bali aj`alny atadabbru ayatihi wa ahkamahu Learning the laws of my religion
Do not let me recite for the sake of recitation , paying no attention to its meaning, but let me contemplate over its signs and commands, to know and understand the modus operandi of Thy religion.
allahumma inni qad qara’tu ma qadayta min kitabika alladhy anzaltahu `ala nabiyyIka alssadiqi salla allahu `alayhi wa alihi falaka alhamdu rabbana
O Allah I have recited that which Thou commands from Thy Book Thou revealed to Thy truthful Prophet, blessings of Allah be on him and on his children. (All) praise be to our Lord.
O Allah let me be one of those who take to the lawful and keep from the unlawful, accept and show submissionto its clear as well as consimilar commands,
and let me be one of those whom Thou shall raise and exalt, on account of this recitation, on the highest pedestal in the Paradise. Be it so O the Lord of the worlds.
Another Dua after reciting quran - following brief supplication that is reported by Shaykh al-Tusi from Imam `Ali Amer al-Mu'mineen (a.s):
اللّهُمّ اشْرَحْ بِالقُرْآنِ صَدْرِي،
allahumma ashrah bilqur’ani sadri
O Allah: (please) expand my breast through the Qur'an
وَاسْتَعْمِلْ بِالقُرْآنِ بَدَنِي،
wasta`mil bilqur’ani badani
And use my body for the Qur'an
وَنَوّرْ بِالقُرْآنِ بَصَرِي،
wa nawwir bilqur’ani basari
And enlighten my sight by the Qur'an
وَأَطْلِقْ بِالقُرْآنِ لِسَانِي،
wa atliq bilqur’ani lisani
And make my tongue eloquent by the Qur'an
وَأَعِنّي عَلَيْهِ مَا أَبْقَيْتَنِي
wa a`inni `alayhi ma abqaytany
And help me carry out its duty as long as You keep me alive,
فَإِنّهُ لا حَوْلَ وَلا قُوّةَ إِلاَّ بِكَ.
fa’innahu la hawla wa la quwwata illa bika
For there is neither power nor might save with You.
Then recite this
Bismillaahir-Rahmaanir-Raheem. Allaahummaa Innee As’aluka Ikhbaatal Mukhbiteen Wa Ikhlaaswal Mooqineen Wa Muraafaqatal Abraari Wa Istihqaaq Haqaaikil Eemaani Wal Ghaneemata Min Kulli Birrin Was-Salaamata Min Kulli Ismin Wa Wujooba Rahmatik Wa Azaaima Maghfiratik Wal Fawza Bil Jannati Wa Najaatam-Minan-Naar.
Imam Ali(as) supplication for memorizing the Holy Quran As-Sahifa Alawiya, Pg.193, Printed in India, Lucknow, 1915
Allaahummar h’amnee bitaraki maa’a’s’eeka abadam maa abqaitanee farh’amni min takallufi maa yai’neenee warzuqnee h’usnal manz’ari feemaa yurz”eeka a’nnee walzim qalbee h’ifz’a kitaabika kamaa a’llamtanee warzuqnee wa atluwahu a’lan naj’willadhee yurz”eeka a’nnee.
O Allah bestow upon me Your mercy so that I am away from Your disobedience always, and bestow the grace that I am not involved in unbearable difficulties, and grant me the goodness for deeds which make You happy with me, and make the memorizing of Your book (the Holy Quran) obligatory on me as You have granted me it’s knowledge, and bestow Your grace so that I recite it in the way Your pleasure is gained.
O Allah illuminate my eyes, expand my breast, illuminate my heart and my tongue flows with the Holy Quran. Give me the strength so that I use my body for the Holy Quran, grant me Your help because there is no helper other than You and there is no god other than You