Dua'a Qunoot

Q. What is dua-e-qunoot?
A. Qunoot, according to the definition of the fuqaha’, “is the name of a du’aa’ (supplication) offered during prayer at a specific point while standing.” It is prescribed in Witr prayer after the rukoo’ (bowing), according to the more correct of the two scholarly opinions.
If a calamity (naazilah) befalls the Muslims, it is prescribed to say Du’aa’ al- Qunoot after standing up from rukoo’ in the last rak’ah of each of the five daily obligatory prayers, until Allaah relieves the Muslims of that calamity.
(See Tasheeh al-Du’aa’ by Shaykh Bakr Abu Zayd, p. 460)

Q2. Is it necessary?
A. 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. Qunoot is Sunnah. Based on this, if a worshipper omits Qunoot, his prayer is still valid.

Q3. Should I recite dua-e-qunoot after bowing or before bowing?
A. 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.

Q4. Till where should I raise my hands?
A. 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

Q5. What is the real dua of qunoot?
A. 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.

It is not obligatory for the du’aa’ of Qunoot to be in the words narrated from the Prophet (peace and blessings of Allaah be upon him); rather it is permissible for the worshipper to say other words or to add to them. Even if he were to recite verses from the Qur’aan that include words of supplication, that would be sufficient.
Many hanafies read - Allahumma inna nasta'inuka wa nastaghfiruka..., which is correct and you can recite that dua.

If you have any further doubts ask under comments.

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For further details and references check the links below
http://islamqa.info/en/9061
http://islamqa.info/en/14093
http://islamqa.info/en/20031