The night prayer or Salat al-Layl is one of the acts of worship and prayers which have been greatly stressed upon and recommended.  With this prayer in the middle of the night close to dawn when there is utter silence and the daily uproar and commotion have seized, one gets a very special state of concentration and excitement which is unique and indescribable. That is, the friends of God always choose the pre-dawn moment for invocation and supplication for they are composed and at rest at this time and there is no intention of showing off. At this time, one gets the best of concentration which extraordinarily helps build and revive the spiritual self. That is why the Holy Quran has promised those who offer the night prayer to grant them a position of great glory (maqam mahmood):

"وَمِنَ اللَّیْلِ فَتَهَجَّدْ بِهِ نَافِلَةً لَّکَ عَسَىٰ أَن یَبْعَثَکَ رَبُّکَ مَقَامًا مَّحْمُودًا"

"And during a part of the night, pray Tahajjud beyond what is incumbent on you; maybe your Lord will raise you to a position of great glory."[1]
How to offer the Night Prayer
The night prayer consists of eleven rak'ats. Out of the 11 Rak'ats of the night Nafilah, 8 Rak'ats should be offered with the niyyat of the Nafilah, 2 Rak'ats with the niyyat of Shaf'a, and 1 Rak'at with the intention of Witr.  All of these  eleven rak'ats can be offered in short and long forms.
Short form:
In the short form of the night prayer, one can suffice to reciting only Hamd, the opening chapter (without Surah) in the prayers.
Long form:
 In this method, in the first initial rak'ats one should recite Hamd followed by a Surah (like Surah al-Kafiroon, Tawhid etc. which have been recommended).  Indeed, according to some traditions, the Surah of Tawhid has been recommended to be recited up to ten times.
When it comes to the rak'ats of Shaf'a prayer, it is better to recite Surah Falaq after Surah Hamd in the first rak'at and to recite Surah Naas after Surah Hamd in the second rak'at. There remains one rak'at of witr prayer in which it is better to recite Surah Tawhid thrice after Surah Hamd along with Surah Falaq and Surah Naas. One can suffice to reciting only Surah Tawhid and then perform Qunut.
Qunut:
The qunut of witr prayer is one of the highly rewarded mustahab acts and stress has been laid on prolonging it. It has been narrated from the Holy Prophet, peace be upon him and his family, that he said: "Whoever prolongs the qunut of his witr prayer in the world, will be at ease at the station of judgment."[2] In Qunut, first pray for forgiveness of forty or more Mu’mineen who are either dead or living in the following manner. For example, you should say:

"اللهم اغفر لفلان

"Allahumma ighfir li-fulan".
Instead of 'fulan', you should mention the name of the individual whom you want to pray for. Or recite:

اللهم اغفر للمؤمنین و المؤمنات

Allahumma ighfir lil-mo'meneen wal-momeenat.

"استغفر الله ربی و اتوب الیه‌"

Then recite seventy times "astaghfirullah rabbi wa atubu elayh." Then recite:

"هذا مقام العائذ بک من النار"

Haza maqamul a'eze bika minan nar.
Then say thirty times:

"العفو"

Al-Afw. Then the following dhikr is recited:

"رب‌ّ اغفرلی و ارحمنی و تب علی‌ّ انک انت التواب الغفور الرحیم‌"

Rabbi ighfirli wa irhamni wa tub 'alayya innka antat tawwab al-ghafoor al-rahim.
Then you should bend for ruku and go down for prostration (sajda) and salam.
Indeed, there are many mustahab dhikr and supplications which one can recite in all the rak'ats of the night prayer. Should you like to learn more about those recommended dhikr, you can refer to special sources or to the following index:
1. Mafatih al-Jenan, late Sheikh Abbas Qummi.

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