Qiyaam' means 'standing' and 'Qiyaam al-Layl' means 'standing in night.' In the Islamic terminology, both terms refer to 'the voluntary night prayer, whose time extends from after 'Ishaa’ (evening) prayer until dawn.' Qiyaam al-Layl is also known as Tahajjud.
A widespread misconception is that Tahajjud is a different night prayer than Qiyaam. The true is that there is only one voluntary night prayer known by different names.
The excellence of night prayer:
Numerous Prophetic narrations and Quranic verses mention the excellence of night prayer and the merit of those who perform it regularly. Allah The Almighty, Says (what means): "O you who wraps himself [in clothing], arise [to pray] the night, except for a little – half of it – or subtract from it a littleor add to it, and recite the Quran with measured recitation."[Quran 73: 1-4]
It is reported that the Messenger of Allah said: “Allah, Our Lord, descends (in a manner befitting His Majesty) to the nearest heaven to us of this universe during the last third of the night and says: ‘Is there anyone to call upon Me so that I shall respond to him (fulfill his prayer). Is there anyone to ask of Me that I may grant his request. Is there anyone to seek My forgiveness so that I shall pardon him (and forgive his sins)’.” [Al-Bukhari and Muslim]
Aa'ishah, may Allah be pleased with her, reported that the Prophet said: “The most beloved deeds to Allah are the most constant, even if they were little” [Al-Bukhari and Muslim], and she, may Allah be pleased with her, said in another narration: “Do not ever stop praying Qiyaam. The Prophet never ceased praying it. When he was sick or weak, he prayed sitting.” [Al-Bukhari and Muslim]
The Messenger of Allah in another Hadeeth, said: "The closest one can be to Allaah The Almighty, is during the last third of the night. If one can remember Allah The Almighty, at this time let him do so." [At-Tirmithi, An-Nasaa'i and Al-Haaqim]
The Prophet also said: “You should pray Qiyaam al-Layl, for it is the habit of the righteous people who came before you, and it will bring you closer to your Lord, expiate for bad deeds, prevent sin, and expel disease from the body.”[At-Tirmithi and Ahmad]
Mu'ath Ibn Jabal, may Allah be pleased with him, narrated that the Prophet said to him: “May I show you the gates of goodness?' (They are) “Fasting is screen from Hell, charity extinguishes the sins as water extinguishes fire, standing in prayer by a slave of Allah during the last third part of a night.” Then the Prophet recited this verse (what means):“They arise from [their] beds; they supplicate their Lord in fear and aspiration…" (Quran 32: 16) [Abu Daawood and At-Tirmithi]
Abu Hurayrah, may Allah be pleased with him, reported that the Messenger of Allah said: “The best of prayer after those prescribed (i.e. obligatory prayer) is that in the depth of night.” [Muslim]
Abu Hurayrah, may Allah be pleased with him, also reported that the Messenger of Allah said: “May Allah have mercy on a man who wakes up at night, prays, and wakes his wife to pray; and if she refuses, he sprinkles water on her face. And may Allah have mercy on a woman who wakes up at night, prays, and wakes her husband to pray; and if he refuses, she sprinkles water on his face.” [Abu Daawood]
Abdullaah Ibn Bashr, may Allah be pleased with him, reported Allah's Messenger saying: “Whoever prays night prayer reciting ten verses, he will not be recorded among the negligent. Whoever prays night prayer reciting one hundred verses, he will be recorded among the devout. And whoever prays night prayer reciting one thousand verses, he will be recorded among those with a multitude of good deeds.”[Abu Daawood]
Again, the Prophet said: "Verily, there is one hour during the (entire) night when any Muslim (submitting to the Will of Allah the Almighty) may call upon Allah and request anything of Him, regardless of whether the matter be worldly or of the hereafter. Allah, theAlmightywill grant and fulfill the request. This is the case every night." [Muslim]
Those who regularly perform the night prayers are the righteous and are more deserving of Allah's bounty and mercy. Allah Says (what means):"Indeed, the righteous will be among gardens and springs,accepting what their Lord has given them. Indeed, they were before that doers of good.They used to sleep but little of the night,and in the hours before dawn they would ask forgiveness."[Quran 51: 15-18]
Allah Says that those who do not possess these qualities cannot be treated as equal to those who possess them. He The Almighty Says (what means):"Is one who is devoutly obedient during periods of the night, prostrating and standing [in prayer], fearing the Hereafter and hoping for the mercy of his Lord, [like one who does not]? Say, "Are those who know equal to those who do not know?" Only they will remember [who are] people of understanding.''[Quran 39: 9]
The following acts are Sunnah (recommended) for the one who wishes to perform the night prayers. Upon going to sleep, one should make the intention to perform the prayers. Abu Ad-Dardaa', may Allah be pleased with him, related that the Prophet said: "Whoever goes to his bed with the intention of getting up and praying during the night, and sleep overcomes him until the morning comes, he will have recorded for him what he had intended, and his sleep will be a charity for him from his Lord."[An-Nasaa'i and Ibn Maajah]
Upon waking, one should wipe one's face, use a Miswaak (toothstick), and make this supplication: "There is no god but You, Glory be to You, I seek forgiveness from You for my sins, and I ask for Your mercy. O Allah, increase my knowledge and let my heart not swerve after You have guided me, and bestow mercy upon me from Yourself. All praise be to Allah who has given us back life after our death and unto Him is the resurrection."
Then, one should recite the last ten verses of chapter 'Al-'Imraan', then one should say, "O Allah, to You belongs the praise. You are the Light of the heavens and the earth and what is therein. And to You belongs the praise. You are the truth and Your promise is true. And the meeting with You is true. And the paradise is true. And the Fire is true. And the prophets are true. And Muhammad is true. And the Hour is true. O Allah, to You have I submitted. And in You have I believed. And in You have I put my trust. And to You have I turned. And by You I argue. And to You do I turn for my decisions. Forgive me of my former and latter sins, and those done in private and those done in public. You are Allah, there is no god besides You."
One should begin the night prayer with two quick Rak'ahs and then may pray whatever he wishes after that. 'Aa'ishah, may Allah be pleased with her, said: "When the Prophet prayed during the late-night, he would begin his prayers with two quick Rak'ahs." [Muslim]
The night prayer may be performed in the early part of the night, the middle part of the night, or the latter part of the night, but after the obligatory 'Ishaa' (evening) prayer.
Anas, may Allah be pleased with him, described the prayer of the Prophet as: "If we wanted to see him praying during the night, we could see him praying. If we wanted to see him sleeping during the night, we could see him sleeping. And sometimes he would fast for so many days that we thought he would not leave fasting throughout that month. And sometimes he would not fast (for so many days) that we thought he would not fast during that month." [Al-Bukhari, Ahmad and An-Nasaa' i]
Commenting on this subject, Ibn Hajar said: "There was no specific time in which the Prophet would perform his night prayer, but he would do whatever was easiest for him."
It is best to delay this prayer to the last third portion of the night. Abu Hurayrah, may Allah be pleased with him, reported that the Prophet said: "Our Lord descends to the lowest heaven during the last third of the night, inquiring: 'Who will call on Me so that I may respond to him? Who is asking something of Me so I may give it to him? Who is asking for My forgiveness so I may forgive him?"'
'Amr Ibn Abasah, may Allah be pleased with him, reported that he heard the Prophet say: "The closest that a slave comes to his Lord is during the middle of the latter portion of the night. If you can be among those who remember Allah, the Exalted One, at that time then do so." [Al-Haakim, At-Tirmithi and An-Nasaa'i]
The number of Rak'ahs (units of prayer) to be performed during night prayer:
The night prayer does not entail a specific number of Rak'ahs which must be performed nor is there any maximum limit which has to be performed. It would be fulfilled even if one just prayed one Rak'ah of Witr after the obligatory night prayer.
Samurah Ibn Jundub, may Allah be pleased with him, said: "The Messenger of Allah ordered us to pray during the night, a little or a lot, and to make the last of the prayer the Witr prayer." [At-Tabaraani and Al-Bazzaar]
One may choose between praying them all together or to separate them. 'Aa'ishah, may Allah be pleased with her, said: "The Messenger of Allah never prayed more than eleven Rak'ahs, during Ramadan or otherwise. He would pray four Rak'ahs, and don't ask about how excellent they were or how lengthy they were. Then, he would pray four Rak'ahs, and don't ask about how excellent they were or how lengthy they were. Then, he would pray three Rak'ahs. I asked: 'O Messenger of Allah, do you sleep before praying Witr?' He replied: 'O 'Aa'ishah, my eyes sleep but my heart does not sleep."' [Al-Bukhari and Muslim]
'Aa'ishah, may Allah be pleased with her, said: "The prayer of the Messenger of Allah during the night would be ten Rak'ahs and then he would make Witr with one Rak'ah."-islamweb.net