Praise be to Allah.
When to recite du'a al-qunut
Du'a al-Qunut is recited in the last rak’ah of Witr prayer, after bowing, but if one recites it before bowing it doesn’t matter. But reciting it after bowing is better.
Shaykh al-Islam [Ibn Taymiyah] said in Majmu' al-Fatawa (23/100):
With regard to qunut: there are two extreme views and one middle (or moderate) view. Some say that qunut should only be recited before bowing and some say that it should only be recited after bowing. The jurists among the scholars of hadith, such as Ahmad and others, say that both are allowed, because both are mentioned in the sahih Sunnah, but they preferred reciting qunut after bowing because this is mentioned more often.
Raising the hands is mentioned in a sahih report from ‘Umar (may Allah be pleased with him), as was narrated by al-Bayhaqi in a report which he classed as sahih, 2/210).
How to offer du'a al-qunut
The worshipper should raise his hands to chest height and no more , because this du'a is not a du'a of supplication in which a person needs to raise his hands high. Rather it is a du'a of hope in which a person holds out his palms towards heaven… The apparent meaning of the scholar’s words is that the worshipper should hold his hands close together like a beggar who asks someone else to give him something.
Should you recite du'a al-qunut in witr prayer all the time?
It is better not to recite qunut in witr all the time , rather it should be done sometimes, because there is no evidence that the Messenger of Allah (peace and blessings of Allah be upon him) did it all the time. But he taught al-Hasan ibn ‘Ali (may Allah be pleased with him) a du'a to recite in qunut al-witr, as will be quoted below.
Formula of du'a al-qunut
The du'a of qunut was narrated by Abu Dawud (1425), al-Tirmidhi (464), and al-Nasai (1746) from al-Hasan ibn ‘Ali (may Allah be pleased with him) who said: The Messenger of Allah (peace and blessings of Allah be upon him) taught me some words to say in qunut al-witr:
“Allahumma ihdini fiman hadayta wa ‘afini fiman ‘afayta wa tawallani fiman tawallayta wa barik li fima a’tayta, wa qini sharra ma qadayta , fa innaka taqdi wa la yuqda ‘alayk, wa innahu la yadhillu man walayta wa la ya’izzu man ‘adayta, tabarakta Rabbana wa ta’alayta la manja minka illa ilayk
(O Allah, guide me among those whom You have guided, pardon me among those whom You have pardoned, turn to me in friendship among those on whom You have turned in friendship, and bless me in what You have bestowed, and save me from the evil of what You have decreed. For verily You decree and none can influence You; and he is not humiliated whom You have befriended, nor is he honoured who is Your enemy. Blessed are You, O Lord, and Exalted. There is no place of safety from You except with You).”
The last phrase – La manja minka illa ilayka (There is no place of safety from You except with You) – was narrated by Ibn Mandah in al-Tawhid and classed as hasan by al-Albani. (Irwa al-Ghalil, hadith no. 426, 429)
Then he should send blessings upon the Prophet (peace and blessings of Allah be upon him). (al-Sharh al-Mumti’ by Ibn ‘Uthaymin, 4/14-52)
What to say after taslim if you recite du'a al-qunut
It is mustahabb to say after the taslim: Subhan al-Malik al-Quddus three times, elongating the vowels the third time, as narrated by al-Nasai (1699) and classed as hasan by al-Albani in Sahih Sunan al-Nasai.
Al-Daraqutni added the word: Rabb al-Malaikah wa’l-Ruh (Lord of the angels and the Spirit), with a sahih isnad. See Zad al-Ma’ad by Ibn al-Qayyim, 1/337.
And Allah knows best.