Du’aa’ al-Qunoot in Witr prayer

Firstly:  

Du’a’ al-Qunoot 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 Majmoo’ al-Fataawa
(23/100): 

With regard to qunoot:
there are two extreme views and one middle (or moderate) view. Some say that
qunoot should only be recited before bowing and some say that it should only
be recited after bowing. The fuqaha’ among the scholars of hadeeth, such as
Ahmad and others, say that both are allowed, because both are mentioned in
the saheeh Sunnah, but they preferred reciting qunoot after bowing because
this is mentioned more often.  

Raising the hands is mentioned in a saheeh report from  ‘Umar
(may Allaah be pleased with him), as was narrated by al-Bayhaqi in a report
which he classed as saheeh (2/210). 

The worshipper should raise his hands to chest height and no
more, because this du’aa’ is not a du’aa’ of supplication in which a person
needs to raise his hands high. Rather it is a du’aa’ 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. 

It is better not to recite qunoot in witr all the time,
rather it should be done sometimes, because there is no evidence that the
Messenger of Allaah (peace and blessings of Allaah be upon him) did it
all the time. But he taught al-Hasan ibn ‘Ali (may Allaah be pleased with
him) a du’aa’ to recite in qunoot al-witr, as will be quoted below. 

Secondly: 

The du’aa’ of qunoot was narrated by Abu Dawood (1425),
al-Tirmidhi (464), and al-Nasaa’i (1746) from al-Hasan ibn ‘Ali (may Allaah
be pleased with him) who said: The Messenger of Allaah (peace and
blessings of Allaah be upon him) taught me some words to say in qunoot
al-witr: 

“Allaahumma ihdini feeman hadayta wa
‘aafini feeman ‘aafayta wa tawallani feeman tawallayta wa baarik li feema
a’tayta, wa qini sharra ma qadayta , fa innaka taqdi wa la yuqda ‘alayk, wa
innahu laa yadhillu man waalayta wa laa ya’izzu man ‘aadayta, tabaarakta
Rabbana wa ta’aalayta la manja minka illa ilayk

(O Allaah, 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 – Laa manja minka illa ilayka (There
is no place of safety from You except with You) – was narrated by Ibn Mandah
in al-Tawheed and classed as hasan by al-Albaani. 

See Irwa’ al-Ghaleel, hadeeth no. 426, 429. 

Then he should send blessings upon the Prophet (peace
and blessings of Allaah be upon him). See al-Sharh al-Mumti’ by Ibn
‘Uthaymeen (4/14-52). 

Thirdly: 

It is mustahabb to say after the tasleem: Subhaan al-Malik
al-Quddoos three times, elongating the vowels the third time, as
narrated by al-Nasaa’i (1699) and classed as hasan by al-Albaani in
Saheeh Sunan al-Nasaa’i. 

Al-Daaraqutni added the word: Rabb al-Malaa’ikah wa’l-Rooh
(Lord of the angels and the Spirit), with a saheeh isnaad. See Zaad
al-Ma’aad by Ibn al-Qayyim, 1/337.